Normal
Defensive-Standard: +3
Defensive-Inverse: 0
Offensive-Standard: -6
Offensive-Inverse: +3
The Best Type.
Defensively, it's OK. It resists Fighting, it's vulnerable to Ghost, that's it. Nobody really cares about that. The real meat is
Perfect Offense. Hits Steel, Rock, and Ghost super effectively, nothing resists it, full stop. (Not even Shedinja walls Normal types, because Ghost is vulnerable to Normal!) Combined with how many low or no-disadvantage hideously powerful Normal moves exist (Boomburst laughs in Draco Meteor's face) and how many Normal types are actually quite good in stats, Abilities, movepool, etc and mostly held back by Normal being a crap offensive type in Standard, Normal is by far the best offensive type in the entire game, even when you consider that Steel is not really worth running defensively and Ghost sucks too.
So yeah. Normal spam is a thing, and there's no proper answer to it.
Fighting
Defensive-Standard: 0
Defensive-Inverse: 0
Offensive-Standard: -4 (Yes, really)
Offensive-Inverse: +1
Defensively, it resists Fairy, Flying, and Psychic. Fairy resistance is pretty irrelevant, but Flying and Psychic resistance, especially Psychic resistance, are both very valuable -Fighting is the only real counter to Psychic, other than other Psychic types! Vulnerability to Dark, Bug, and Rock are all problematic -these are all types with substantial offensive use, and even with Stealth Rock being less popular in Inverse than in Standard, it's still a bad thing to be vulnerable to it. (Lucario sux, 50% health lost to Stealth Rock, no recovery beyond Drain Punch, Steel is awful in general)
Offensively, Fighting is resisted by Steel, Rock, Normal, Dark, and Ice -other than Steel, these are all relevant defensive types, so Fighting has some flaws as an offensive type. On the other hand, it hits Psychic, Flying, Bug, Poison, Ghost, and Fairy effectively -Psychic is huge, since Fighting is it other than Psychic itself for hitting Psychic effectively, Flying is quite relevant, and even Bug has relevance. (Mega Heracross has some pretty good value in this meta, for instance) Ghost, Poison, and Fairy are lot harder to appreciate the value of -they're all three severely flawed (Read: godawful) as defensive types, with little motivation to run them. In short, Fighting is less amazing an offensive type as in Standard, but it's still a crucial offensive type.
Again: the only counter to Psychic that exists. (Unless you count Shedinja I guess, but it's got more weaknesses than ever -most Psychic types should have some way to break it)
Psychic
Defensive-Standard: -1
Defensive-Inverse: +1
Offensive-Standard: -4
Offensive-Inverse: +1
Oh, to return to the halcyon days of Generation I, when Psychic was The Best Type, with only one type other than itself that acted as a counter... oh, wait, that's called Inverse.
Defensively, Psychic only has two weaknesses -itself and Fighting. Meanwhile it resists Dark, Ghost, and Bug, all of which are good types to resist. So only Fighting types are actually a counter, other than other Psychic types. (That preferably are Fighting or Poison typed -oh by the way, there is no Psychic/Poison Pokemon, and Poison sucks anyway)
Offensively it hits Dark, Steel, and itself super effectively, with only Fighting and Poison resisting it. It's super effective list isn't actually amazing -the Dark hit is useful- but Poison is godawful, leaving Fighting as the only real counter to Psychic. Alarmingly, there are a number of Psychic types with Dark, Bug, or Rock moves they can properly use to counter this counter, making it very difficult indeed to properly wall Psychic types -Gothitelle is a nightmarish trapper, being extremely difficult to KO and with Dark Pulse allowing it to finish off slower Fighting types if it wants. (Though it's probably better off running Energy Ball to deal with Poison, Grass, Bug, and yet other types, and it's difficult to justify three attacking moves on Gothitelle)
If it weren't for Normal, Ice, and Grass being amazing in their own ways, I'd just declare Psychic The Best Type. It's pretty nutty.
Dark
Defensive-Standard: +3
Defensive-Inverse: 0
Offensive-Standard: -1
Offensive-Inverse: +1
Resists Bug, Fairy, and Fighting. Resisting Fairy isn't actually that useful (See the Fairy entry below), but Bug is a very relevant offensive type and Fighting is huge, since Fighting is the only proper counter to Psychic types, which renders it very important to have Fighting counters -Rock can also do the job, but is more deeply flawed than Dark is, being weak to Normal. (On the other hand, Rock additionally resists Grass, Water, and Ground, so Rock certainly has arguments in its favor) Conversely it is weak to itself, Ghost, and Psychic, all of which hurts to be weak to. Tricky.
Offensively, Dark is only resisted by Psychic and Ghost. Being resisted by Psychic hurts, since Psychic is one of the best types in the game, but being resisted by Ghost is actually something of a laugh -Ghost types are really, really bad in Inverse, for all that Ghost moves are hugely important. Meanwhile it hits itself, Fighting, and Fairy all super effectively -the big one from the perspective of Dark type Pokemon is the effectiveness against Fighting types, though it certainly hurts that, for instance, Conkeldurr can use Knock Off for a super effective hit even though you resist it and are super effective, while Fairy is somewhat ignorable, as Fairy is painfully bad.
A very important type in general. I've personally been amused by how Tyranitar retains essentially it's weird position in Standard, but flipped around -either way it's an important Pokemon with problematic weaknesses and yet uniquely useful strengths. It just replaces a double weakness to Fighting with a single weakness to Normal -which is enough, when Normal gives us moves like Last Resort and Boomburst, not to mention Explosion.
Fairy
Defensive-Standard: +3
Defensive-Inverse: -2
Offensive-Standard: 0
Offensive-Inverse: 0
Defensively, its only resists are to Poison and Steel, and while they're both useful coverage types, not many actual Pokemon of those types are liable to show up, so that's a problem. (And many Poison types are also Bugs -Mega Beedrill will just U-Turn you out of existence) Worse yet, it's vulnerable to Bug, Fighting, and Dark, all of which are relevant offensive types, and it's also weak to Dragon, which has the advantage that only Dragon resists Dragon. It's very hard to argue for Fairy types from a defensive standpoint, in short.
Offensively, Fairy is good against Steel (So's everything else) Fire (Still a ton of things) and Poison (Also a ton of things) while being resisted by Dark, Fighting, and Dragon. It's a really redundant, unappealing offensive type. This makes it even harder to argue for actually using Fairies.
Really, Fairy is kind of just a crap type.
Ghost
Defensive-Standard: +8 (Two immunities!)
Defensive-Inverse: -2
Offensive-Standard: -3
Offensive-Inverse: 0
Defensively, one of the worst types of the meta. Literally it's only positives are resisting itself and Dark, while it's vulnerable to Normal, Fighting, Bug, and Poison. This is godawful, and really the only good arguments for Ghost types are A: they can't be trapped (Anti-Gothitelle work) and B: they are STAB super effective against Normal types. So many Ghosts imagine themselves to be walls this is a deep problem -though Gengar doesn't care, just like it never cares. It's always a good Pokemon in any meta.
Offensively Ghost has the crucial, crucial utility of being anti-Normal -the only type in the game, making the common access Psychic types have to Shadow Ball very valuable indeed. It additionally hits Dark effectively, with the only things that resist it being itself and Psychic, so it remains an excellent offensive type. (Fighting/Ghost remains perfect coverage, for instance)
Flying
Defensive-Standard: +4
Defensive-Inverse: -1
Offensive-Standard: 0
Offensive-Inverse: 0
Crucial as a resist to Electric, with the only other option being Water, and its resistance to Ice and even Rock are actually pretty useful. (Remember, even though Flying types are vulnerable to Ground, they're still not grounded, so most Flying types resist Stealth Rock and are immune to Spikes and Toxic Spikes) It's vulnerable to Bug, Grass, and Fighting, which is pretty horrifying given how powerful Grass is, how crucial Fighting is, and how appealing Bug can be, and it's also vulnerable to Ground, which is problematic when it's one of the best anti-Grass types around and Grass is so important. Yet, it's still a valuable defensive type.
Offensively, it's resisted by Bug, Grass, and Fighting, which sucks, though combined with the right coverage it's manageable. It's super effectives are Rock, Steel, and Electric, which isn't great. Its real problem as an offensive type is that Normal is always better unless you're dealing with an Electric type. (That is not also Bug, Grass, Fighting, or Ghost, at that) To be fair, while Electric has more weaknesses than strengths, those weaknesses are only Flying, Electric, and Steel, so Flying is the only proper counter to Electric types, other than Electrically immune Electrics. (Whom are not mutual counters, obviously) So there's that.
Also the ability to Roost your typing out of existence gives Flying the ability to wall threats it really shouldn't be able to, so its degree of vulnerability is misleading.
Bug
Defensive-Standard: 0
Defensive-Inverse: 0
Offensive-Standard: -4 (In spite of nothing being immune to it)
Offensive-Inverse: +4
Defensively, Bug hasn't changed in quantity, just distribution. Unfortunately, being vulnerable to Grass and Fighting is quite painful, and sharing Ground weakness with Grass is also quite painful, while its resistance to Fire and Flying is shared with Grass as well, leaving it with resistance to Rock over Grass. This is seriously limiting its appeal as a defensive type.
Offensively, it hits 7 types super effectively and is only ineffective on three types -unfortunately, the distribution has problems, with the important and powerful Psychic and Grass types being included among the resists (And even Dark has value), while many of the super effectives are severely flawed in other regards, or shared with Grass, such as Poison. (Yes, Bug hits Ghost effectively, but so does Normal, with better moves) It does hit Fighting super effectively, though, giving it value to Psychic types looking for Fighting coverage (And it provides Poison coverage, too!), such as Alakazam appreciating its access to Signal Beam, and is in fact perfect coverage alongside Psychic. (Though no Psychic type does better than Signal Beam, and Physically Mew, Gallade, and Arceus are the only Psychic types with so much as X-Scissor)
Most painfully, U-Turn is ineffective against the trapper Gothitelle. Bug types themselves aren't very good, in short -which is problematic, when Bug coverage is hard to come by outside of U-Turn. Note that the classic crapmon combo of Bug/Flying has gotten even worse, trading its double weakness to Rock in standard for double weaknesses to all of Grass, Fighting, and Ground in Inverse! Sure sure, you double resist Stealth Rock. Whatever.
Even so, Bug is an important type, especially offensively.
Grass
Defensive-Standard: -1
Defensive-Inverse: +1
Offensive-Standard: -4 (Again, with no immunities)
Offensive-Inverse: +4
The Best Type, other than Normal. Resists a ton of types, including the very relevant Ice and Bug types, while it's only weaknesses are itself, Water, Electric, and Ground -Water being almost 100% a bad Grass offensively, Electric has severe problems, and Ground... is actually pretty good, OK.
Offensively it's only resisted by Ground, Rock, and Water, and has seven super effectives. If Normal weren't the obvious king of offense, I'd argue Grass is the best offensive type in the game, alongside Bug -it's still a fantastic offensive type even then, the sort of thing that Normal types wish they could run as additional coverage. (Farfetch'd is the only Normal type with Leaf Blade, and the pool of Normal types that gets Energy Ball or Giga Drain is tiny... and for some reason includes Zangoose with Giga Drain, who really shouldn't be running a weak Special move, even if it does make Dragonite cry)
Gogoat is particularly notable, alongside Sawsbuck (Which is also the dreaded Normal type) as Grass supremacy Pokemon -Sap Sipper renders them immune to Grass, but they can hit back with STAB super effective hits, not to mention placing them at 5 resists, one immunity, three weaknesses, which is very impressive for Inverse. Also notable is Carnivine, as a Levitating Grass type, so Carnivine laughs in the face of Ground types that think they constitute a counter.
Electric
Defensive-Standard: +2
Defensive-Inverse: -2
Offensive-Standard: -6 (A good example of how this simple scoring system has problems)
Offensive-Inverse: +4
Defensively, only Steel is worse. It resists Ground (So does a bunch of other stuff), and it's vulnerable to itself, Steel, and Flying. On the other hand, it actually doesn't have to worry too much about Normal types slamming it with coverage, and Diggersby is one of the more popular Normal types around.
Offensively, it's amazing, with only Water (Very niche) and Flying (Mostly notable for resisting it) offering any protection without turning to Abilities. On the other hand, some Pokemon get Electric immunity via Ability that would normally be vulnerable, specifically Rhyperior, Marowak and Mega Sceptile, and they have actual appeal in Inverse.
The fact that various Electric types get Electric-immunity on Abilities is actually quite good, giving those Pokemon two weaknesses, one resistance, one immunity, which isn't half-bad, especially since Electric is actually a very powerful coverage type in this that most Pokemon can get a hold of.
The Rotoms (And Eelektross) are of course something of a mockery -but Mowtom and Fantom at least get some use out of Levitate now.
Fire
Defensive-Standard: +3
Defensive-Inverse: -3
Offensive-Standard: 0
Offensive-Inverse: 0
An enormous number of weaknesses, of which only maybe Fairy is ignorable. And yet, it resists all of Ground, Rock, and Water, the former two being rather important.
Offensively it's painfully bad. It's resisted by the excellent Grass, Bug, and Ice types, throwing in failure against Steel types for laughs, and meanwhile the things it's good against are itself, Water, Dragon, and Rock. Half of these are done better by Grass, Rock is done better by Normal, and Water is better handled by Ice.
I suddenly understand why I've never seen a Fire type in Inverse unless the team's creator was completely clueless about Inverse.
It's difficult to even argue that the assorted Flashfire Pokemon are well off -the only two Standard-competent abusers are both vulnerable to Normal, and the vast majority of the rest are low-stat and/or saddled with other problems.
Water
Defensive-Standard: +2
Defensive-Inverse: -2
Offensive-Standard: 0
Offensive-Inverse: 0
Defensively, it's bad, particularly since Fire and Ice are very relevant offensive types, and even Steel has uses. Crucially though, it resists Grass and Electric, only one of two types that resists the latter, so that's big and might win a Water type a spot on your team.
Offensively, I can reverse a statement I've made several times elsewhere -in Inverse, it's a bad Grass type, except when it comes to other Water types. This is even worse than it sounds when you consider how many Water types get Ability-based immunity to Water moves -so barring Mega Gyarados slamming into them, they essentially invalidate the notion of Water being anything other than a good STAB offense. Ouch. (Oh and for Mega Gyarados that is a STAB offense)
It's not even practical to say that the Water types that get Water Absorb or Storm Drain are good Water supremacy Pokemon -Seismitoad, Rotom-Wash, and Keldeo are the only fully evolved Water types that don't get Ice Beam, so you have to be talking something like Storm Drain Gastrodon for them to not just turn to Ice Beam or similar. So basically some of them (Cradily, mostly) might work as a Keldeo counter. (To be fair, Keldeo is still a quite good Pokemon in Inverse)
Ice
Defensive-Standard: -3
Defensive-Inverse: +3
Offensive-Standard: 0
Offensive-Inverse: 0
Wallin' everything forever. Only weak to itself, making it a crucial offensive type too. Probably it's biggest flaw offensively is that Grass resists it, but it's not that hard to get around that -Avalugg gets Earthquake, for instance.
Not much to say. It's a great type.
Ground
Defensive-Standard: +3
Defensive-Inverse: 0
Offensive-Standard: -1 (It hits so many things that even with immunities rated at -4 it's nearly 0)
Offensive-Inverse: -2
Resists Grass, Water, and Ice, which are all excellent resistances to have. Vulnerability to Poison isn't so bad, vulnerability to Rock isn't so bad (Rock types are very difficult to use properly when Normal spam is king), and vulnerability to Electric is somewhat odd -on the one hand, Electric is only not the worst defensive type because Steel is even worse, but on the other hand Electric has gone from having two important offenses but actually a bad total offensive capacity to being widely effective and with only two things resisting it, so Electric is actually a fairly good offensive type. Ground is, in short, a really good defensive type with manageable weaknesses. Use Hippowdon people!
Offensively, the main thing you can say for it is that it hits both Bug and Grass super effectively, which are both important types to hit. It's resisted by five types, and even considering that only Rock and Fire are the particularly relevant types that's still mediocre, and Fire is actually really good in Inverse, so that's a problem, especially since Ground types struggle to actually get anti-Fire coverage.
A good type overall, in short. Useful coverage against Grass types for some types. (eg regular Heracross appreciates its access to Earthquake [Mega Heracross has Bullet Seed for 25% more power]) Also keep in mind that Marowak and Rhyperior can be immune to Electric via Lightning Rod, reducing their weaknesses some -Marowak in particular ends up only weak to Rock and Poison at that point.
Rock
Defensive-Standard: -1
Defensive-Inverse: +1
Offensive-Standard: +1
Offensive-Inverse: -1
For all that it's points value goes up in Inverse, in practice it is severely hurt by being vulnerable to the omnipresent and omnipotent Normal types. It's also vulnerable to Fire, which is not great. On the other hand, it resists Fighting and Grass, both of which are important types, so it might be worth putting on your team as your anti-Fighting answer. Unfortunately Archeops (U-Turn) and Probopass (Volt Switch) are the only Rock types that are good at switching out of trouble productively (Get a hit in on the Ambipom that's switching in) and they both have severe problems.
Offensively Rock is in an odd place. It's resisted by Bug, Ice, Flying, and Fire, none of which is a good thing to be resisted by, but it's crucial for hitting Fighting and Ground types super effectively. It's a good coverage move anyway, even in Inverse, particularly for the likes of Ice and Psychic types. Slowking, Starmie, and Grumpig are all Special Psychic types with Power Gem, while Gallade, Mew, and Claydol are all reasonably competent users of Physical Rock moves, in both cases for anti-Fighting work. Avalugg, Mamoswine, Beartic, Walrein and Abomasnow are all reasonably competent Ice users of Physical Rock, though unfortunately no Ice type exists that has Power Gem.
Steel
Defensive-Standard: +11
Defensive-Inverse: -8
Offensive-Standard: -1
Offensive-Inverse: +1
Godawful.
OK, offensively it's worth some commentary, since plenty of Pokemon get Iron Head as coverage and some get Flash Cannon. Specifically, it hits Fire, Water, and Electric (Also itself but everything does) for super effective damage, with only Rock, Ice ("Only" Ice he says), and Fairies resisting it. So Chesnaught might run Iron Head for those pesky Water and Electric types, Thundurus might run Flash Cannon for Water types, etc. Not unusable offensively, in other words, though it really hurts its case that Ice resists it given that Ice is the king of defense in Inverse.
Poison
Defensive-Standard: +3
Defensive-Inverse: -3
Offensive-Standard: -6
Offensive-Inverse: +3
Crucial resistance to Psychic -it's the only thing other than Fighting that does resist it- and its resistance to Ground is also OK, though that's very commonplace. Unfortunately, it's a godawful defensive type, with all that really needs to be said being that it is vulnerable to both Bug and Grass -that's horrible. Offensively, it's more impressive, with only Fairy and Grass resisting it and a bunch of super effectives -but those include Rock (More terrified of Normal), Ghost (More terrified of Normal), Steel (More terrified of Normal) itself (Bad defensive type) and Ground. (Actually worth noting, since Electric and Rock are the only other options and they have severe problems themselves)
Probably Poison's biggest problem is how many of them desperately want to wall -but for the aggressive ones, this may well be a very good meta for them. (I'm honestly surprised at how rarely I see Crobat)
Crucially, it provides perfect coverage to Grass, so Grass/Poison is actually a very strong typing. In general it's actually a pretty nice coverage type.
Dragon
Defensive-Standard: +1
Defensive-Inverse: -1
Offensive-Standard: -4
Offensive-Inverse: +1
A bad defensive type in Inverse, and in spite of the +1 rating a bad offensive type in Inverse too -it's only effective against Steel (So's everything else) and Fairy. (Which is a shockingly bad type in Inverse) It does only falter against itself offensively, so Dragon is arguably back to pre-Gen VI "Outrage everything to death" mode, except Normal blows it out of the water for that type of nonsense. (And it gets Thrash to do the exact same thing) Defensively it's vulnerable to the excellent Water and Grass types, as well as Fire and Electric while you're at it, with it's only positive qualities being it resists itself (It's not a good offense type, barring Draco Meteor), it resists Fairy (Fairy sucks), and it resists Ice. (This is actually useful -but there are better types with that quality)
Probably Dragon's biggest problem is how heavily it overlaps with Grass -yes, Grass. They share three weaknesses, with the only weakness Grass has that Dragon doesn't being Ground (Carnivine laughs at the idea that this helps Dragon's case), and the most useful resistance Dragon has -Ice- is also shared with Grass, leaving it with being useful for Fairy resistance (Dark and Fighting both do it as well while being very important and useful types in their own right) and resisting itself.... which runs into the self-reinforcing loop problem that Dragon is too crappy for it to be worthwhile to carry a Dragon for Dragon resistance. Remember, almost any team prepared for Grass (And that's going to be pretty much any sensible team) is incidentally prepared to annihilate your Dragon, high BST or no.
Goodra's access to Sap Sipper is actually very notable in Inverse, turning Dragon's most unbearable weakness into a stat-boosting immunity. Still got problems compared to the likes of Gogoat and Carnivine.