Kyle Broflovski:
Active: Can send people and objects into limbo and bring them back out.
Passive: Very, very good vision, especially when it comes to aiming. Keen hearing.
Weapon: With the bow, he can shoot an arrow and manipulate it's matter into being multiple arrows.
Stan Marsh:
Active: Super strength when channeled.
Passive: Can take more damage/tougher than the others.
Weapon: With his sword, he can deal powerful blasts that will stun enemies and throw them back a few feet.
Eric Cartman:
Active: Can stun enemies with a flick of the wrist, but it drains his energy.
Passive: Psychic, can see one week into the future.
Weapon: With his staff, he can summon blue energy strikes to nearly kill an enemy.
Kenny McCormick:
Active: He can spawn wings, but it'll drain his energy to near death. He can use his charm to distract enemies.
Passive: Immortality. Also, the ability to speak to animals.
Weapon: With his bow, he can either kill, or stun an enemy. He doesn't get to choose whether he stuns or kills.
Leopold Stotch:
Active: Healing powers.
Passive: All attacks are weaker than everyone else's.
Weapon: With his Hammer of Chaos, he can use lightning strikes, and transform into Professor Chaos, which will drain all of his energy to near death.
Additional Notes:
powers were created mainly with Stick of Truth abilities in mind.
when Kyle uses his limbo powers, his eyes go black with white flecks in them, like stars and a black sky. ((i believe this is mentioned in the first chapter))
Q/A:
Q: Why can Kyle send things into limbo?
A: In "Tooth Fairy's Tats 2000", Kyle basically broke the universe near the end of the episode. Since then, Kyle has been able to manipulate objects to make them disappear or reappear.
Q: Why does Kenny get wings?
A: I have no idea. I have a wing fetish. Also, he's been remarked as "the boy with the broken halo" or a fallen angel for his immortality.
Q: Why does Stan have super strength?
A: I had to pry into the aesthetics of his Stick of Truth persona; his abilities are mostly just "hitting things really hard with a sword".
Q: Why does Kyle have better hearing/eyesight than the others?
A: His Stick of Truth persona is an elf, and canonically, elves are archers. Archers tend to have more refined sight and hearing skills. Also, he's an archer, and, see sentence before.
Q: Why are Butters' attacks weaker than the others?
A: His persona on the show is small, timid and shy. In the Stick of Truth game, his health and attacks are lower than the others, and his energy is drained faster. Because of this, it's become fanon/kinda canon that Butters is pretty small in size.