Mortal Kombat Trilogy
Go to the OPTIONS menu and hold Up + Block + Run until the screen shakes.
At the character select screen, highlight Sonya and press Up+Start. After you select your character, you can then toggle through the backgrounds to choose the one you want.
Play as Chameleon:
To play as Chameleon choose any male Ninja at the character select screen. Press and hold Left, High Punch, Low Punch, Run and Block until the match starts.
MK Classic Fighters:
In the player select, highlight any one of these characters; Kung Lao, Kano, Raiden or Jax and press Select for play with classic fighters.
Thanks to Revolution readers Jim Hirabayashi and Nicolas Mendez!