Question

This guy reminds me of my cat (in terms of body weight.) Mine has the ability Thick Fat and is EV trained in Defense. It knows:

Attract: I don't know what could possibly be attracted to this thing. Causes infatuation.

Body Slam: Good power, STAB, high accuracy, good chance to paralyze.

Swagger: Confuses the foe. Works well with Attract.

Charm: Gets rid of the attack the foe gained with Swagger.

Purugly learnset

Answer 1

Body slam- good chance for paralysis

shadow claw-good unexpected attack, good critical hit chance

aerial ace-covers fighting weakness

attract-catches unsuspecting foes off guard

Answer 2

This is my Taunt-Lead Purugly, I use it on my Mono-Normal team. It's a little gimmicky, but here's the set:

Purugly (F) @ Focus Sash
Trait: Thick Fat
EVs: 72 HP / 184 Atk / 252 Spd
Jolly Nature (+Spd, -SAtk)
- Super Fang
- U-turn / Sucker Punch
- Taunt
- Toxic
Thick Fat is the only really useful ability here, it gives a normally neutral Purugly a couple of free resistances.
Super Fang deals 1/2 health instantly, it can really cripple just about anything. U-Turn can switch out to something that can finish a wounded opponent, or Sucker Punch can hit with priority and do some damage. Taunt stops set up and recovery that would make Super Fang pointless, it is the most important move in the set and should always be used first turn. Toxic is another crippler and great to irritate an opponent right from the get-go.
EVs give a 301 HP stat to deal with stallers who use Seismic Toss. Speed is the most important, as it gets the Taunts and Super Fangs out quickly, while the rest is in Attack to deal heavier damage on the Turn or the Sucker Punch. This Pokemon also works really well with someone who uses Entry Hazards.

Answer 3

Purugly @ Leftovers
Trait: Thick Fat
EVs: 4 HP/252 Atk/252 Spd
Adamant (+Atk, -SAtk) or Jolly (+Speed, -SAtk)
- Body Slam/Slash
- Wake-Up Slap/Bulldoze/Aerial Ace
- Shadow Claw
- Hone Claws/Fake Out/Sucker Punch
Body Slam or Slash is for STAB. Wake-Up Slap is for Rocks and Steels, but…so is Bulldoze, which lowers everyone’s Speed and…doesn’t wake them up. Aerial Ace is for…Fighting types? Yeah, that’s the only reason to use it. Shadow Claw is for Ghosts the Body Slam, Slash, Wake-Up Slap and sometimes Bulldoze cannot hit. Hone Claws raises Attack and accuracy, but Fake Out or Sucker Punch are both good options.

Answer 4

Gen V

Purugly (F) @ Life Orb
Trait: Thick Fat
EVs: 4 HP / 252 Atk / 252 Spd
Adamant Nature (+Atk, -SAtk)
- Sucker Punch
- Fake Out
- Hypnosis
- Bulldoze