Level 100 Statistics (see level 5, 50, 100)
We'll take a generic Water-type, give it crummy stats EVERYWHERE except for Speed, give him a trait that doubles his Speed in the rain and the option to use Agility and call it a day. Luvdisc is great if you're playing with Battle Timeout, because its mere presence should cause your opponent to laugh at it for so long that you win the match.
Such a load of potential here. First off, use Rain Dance to double the only stat that Luvdisc doesn't need a boost in. 95 Base Power with the boost from STAB and Rain Dance sounds very powerful, and it would be on any other Pokémon. Ice Beam is for all these Grass-types that have way too much Special Defense to hurt anyway, but I suppose I just like the words "It's super effective" on your screen. Toxic shows off Luvdisc's amazing stalling power with 43 HP, 55 Defense and 65 Special Defense, but Hidden Power Electric is there if you're afraid of Pelipper or (God forbid) a hostile Luvdisc!
Watch Luvdisc stall out his opponents with his amazing total of defenses not even topping 170. Confusion and attraction together equals a 75% chance your opponent has to wait one more turn before Luvdisc is turned into a pile of heart juice, Protect is another turn, which means that Toxic might inflict a little damage in the meantime. If you're lucky. Aqua Ring can be used on this set. Just kidding, of course.
Get to 1 HP somehow and start Flailing. Your third move is here to add more Speed should you run into one of the three or so Pokémon Luvdisc should ever face that actually outspeed him. Safeguard prevents you from being statused (because such a tank as Luvdisc is obviously going to get Toxiced and all...), or you could use the Water moves and hope to make a use out of Rain Dance and actually hurt Rock-types like Sudowoodo. If by hurt you mean tickle.
Charm turns Luvdisc into a very sturdy physical wall that can survive two Caterpie Tackles and force it to switch out.
Checks and Counters
Instead of listing Luvdisc's counters, I'll list here what doesn't counter Luvdisc: