Name: Regice
New Typing: Ice/Electric
New Abilities: Analytic/Heatproof
New Stats: 80/50/120/120/200/20
Movepool Additions: Recover, Volt Switch, Wild Charge, Energy Ball
Justification: I'm giving all the golems part Electric-type, which their glowing eyes should be suffice to represent - at the same time, their robotic-like look lead to me giving them Analytic. Regice here gets Heatproof as the HA due to its pokedex: "Its icy body is so cold, it will not melt even if it is immersed in magma." Recover is kind of Regirock's thing, but since they're all said to be man-made, it isn't too much of a stretch to assume that they can all repair themselves. Energy Ball is more of a genetic energy-based move than Grass-type specifically, which is why I don't feel there's any problem giving it that.
Niche in OU: STAB BoltBeam? STAB BoltBeam.
While Ice is still a terrible defensive typing, Electric-type gives it some more resistances, remove the Steel-type weakness and gives a Ground-type weakness in return. Having Energy Ball to cover those Water/Ground or Ice/Ground mons, it can effectively work as a special tank, hitting extra hard with Analytic, or a more defensive variant with Heatproof eliminating its Fire-type weakness. It's still weak to Stealth Rock, but Recover helps with that immensely. Furthermore, it can now do a slow Volt Switch out, allowing a teammate to switch in safely.
Name: Regirock
New Typing: Rock/Electric
New Abilities: Analytic/Solid Rock
New Stats: 80/120/200/50/120/20
Movepool Additions: Recover, Volt Switch, Wild Charge, Magnet Rise
Justification: See Regice for the reasoning for Electric-type and Analytic. Solid Rock, well, Regirock is literally a pile of rock. How much more flavorful can you get? Recover is based on Regirock's pokedex entry: "If this Pokémon’s body is damaged in battle, it is said to seek out suitable rocks on its own to repair itself." As for Magnet Rise? I'm pretty sure it has some magnets hidden in those rocks of it.
Niche in OU: Similar to Regice, it now has another STAB to take advantage of, and while the 4x weakness to Ground is rather crippling, it can use Magnet Rise on a predicted switch to take care of that issue. Recover gives it further longevity, allowing Regirock to act as a pretty good tank, especially with Solid Rock alleviating its weaknesses. Analytic is an option if you want more power, but Regirock can be hurt pretty badly without Solid Rock's protection.
Name: Registeel
New Typing: Steel/Electric
New Abilities: Analytic/Bulletproof
New Stats: 80/90/155/90/155/20
Movepool Additions: Recover, Volt Switch, Wild Charge, Knock Off
Justification: See Regice for reasoning behind Electric-type, Analytic and Recover. Bulletproof isn't completely flavorful, but it's based on the pokedex: "Its body is said to be harder than any kind of metal." Knock Off is really just a generic move, to be honest.
Niche in OU: Now, with Recover and Bulletproof in hand, Registeel can sit in front of quite a lot of special attackers due to its immunity to Focus Blast and Shadow Ball. Well, as long as they don't carry Ground-type coverage, that is. Other than that, It can comfortably take most attacks and simply Recover off the damage, and then fire back a powerful Gyro Ball off the incredibly slow 20 Speed. It can even run a Curse Set with Gyro Ball and Thunder Punch/Knock Off, hitting off its decent 90 Atk/SpA.
Name: Regigigas
New Typing: Normal/Ground
New Abilities: Sheer Force/Unaware
New Stats: 105/155/100/60/100/70 (BST 590)
Movepool Additions: Whirlwind, Rest, Slack Off, Bulk Up
Justification: Regigigas is said to tow the continents, so a Ground subtype isn't out of the blue; It also plays to the shared Electric-type of the Regis, signifying that Regigigas is the trio leader. Sheer Force because you're going to need some really strong force to pull continents, and Unaware is sort of a succesor to Slow Start, as Regigigas is shown to be standing in a temple, almost statue-like, without caring about moss growing on it.
Now, as for the moves: Rest is really just there because Regigigas doesn't learn it despite it fitting flavor so much, Slack Off is sort of in the same vein, and its body is bulky enough to learn Bulk Up. And Whirlwind makes sense, I swear! Well, as much sense as Snorlax, Grumpig, Rampardos and Hippowdon learning it does.
Niche in OU: With this, you get either an incredibly bulky nuke with Sheer Force to boost its coverages, or an Unaware tank/wall with offensive presence. With 105/100/100 bulk, it can set up Bulk Up with ease, with STAB Return and Earthquake plus Knock Off for perfect coverage. You can do RestTalk, defensive, Bulk Up with Slack Off, Assault Vest, Band, maybe even Scarf - only thing holding back it is the weaknesses to the common Fighting-, Water- and Ice-type moves.