Violet and Mike's defeat animations have them falling over.
Judy when utilizing her Purple "Play Dead" skill. She essentially re-enacts the "blood and death" opening scene from her movie, complete with a ketchup bottle, before springing back to life.
Stitch's victory animation has him put on a grass skirt, put his hands up, and "hula" for a few seconds like in the current image of Lilo & Stitch's funny moments page.
Sulley's defeat animation has him fainting, in reference to a scene when he thought Boo was getting crushed in the trash compactor in Monsters, Inc.
Moana's defeat animation has her failing to catch her oar she was spinning.
The Queen Of Hearts' defeat animation has her tumble backwards and her dress fall down, revealing her heart-print underwear.
Merlin enters in his Bermuda outfit. His defeat animation is him yelling "BLOW ME TO BERMUDA!" and promptly rocketing away.
Goofy enters by walking backwards, falling over, and getting back up. His defeat animation has him slipping and falling.
Anger's victory animation has him repeatedly mimic a train's whistle with appropriate facial expression (which references a scene from Inside Out).
Huey, Dewey & Louie's defeat animation has Huey placing his hands over his eyes, Dewey placing his hands over his ears, and Louie placing his hands over his mouth, in reference to the Three Wise Monkeys pictorial.
Linguini and Remy's defeat animation has them accidentally tossing the pan in the air, in reference to them accidentally throwing the pan out of the window in Ratatouille.
Friendships
Mike and Sulley's friendship campaign involves them putting on a comedy show to gather enough laugh energy from The City to deal with some blackouts. Some people they recruit include the Genie and Mushu. Just the thought of those two putting on a comedy routine is pretty funny by itself.
Applies In-Universe as well: apparently, they generated enough laugh to power the entire City for years to come!
Stitch and the Mad Hatter's friendship campaign is just as madcap as you'd expect; upset that he doesn't have a birthday, Stitch and the Mad Hatter arrange an unbirthday party for the former by stealing various items from other characters — furniture from the Beast's castle, tea from John Smith and cakes from Remy and Linguini. By the end of the campaign, all of the parties the two stole from return to get their stuff back - Beast with raw beastly fury, John Smith with his army and Remy with an army of rats.