I think Annie is just prancing in daisy fields with her teddy and then gets yanked into an ethereal plane before being forced onto the Fields of Justice! The time warp leaves her delirious and that's why she insists on other to play with her and continues skipping around. I believe she also doesn't understand why everyone keeps trying to kill her, that's why she is looking for her bear Tibbers to ask. Of course, once and awhile he shows up to protect her.
I believe Nidalee is in a forest rolling around the leaves with her fellow felines!
Amumu is probably crying himself to sleep in his pyramid.
Corki is in theatre and re-enacting the World War I, starring as Manfred von Richthofen, a.k.a. Red Baron.
Gangplank and Gragas I believe are in business together really, rather than what lore says. I think Gragas is a be time supplier for Gangplank and his fellow pirates' ale.
Twitch, I honestly believe he is just some kind of perv, since he is always stealthed. He is probably spying on all the innocent daughters and wives out there, that creepy jerk.
I feel Udyr, if I'm right, runs a dojo in some town and trains Akali and Shen for upcoming matches.
Teemo is busy digging holes and hiding all the ears he got from his victories (ears; look up Diablo 2)
That's all I have on the 411 for now, more later.