To access the Cheat Menu:
At the screen where Exor bellows "Midway presents WARGODS!!" press Right, Right, Right, B, B, A, A.
To play as Exor:
At the character select screen press Left, Down, Down, Right, Left, Up, Left, Up, Right, Down
To play as Grox:
At the character select screen press Down, Right, Left, Left, Up, Down, Right, Up, Left, Left
At the title screen press C left ,C left, R, A, B, C up, C right
Thanks to Revolution readers Matt and SoulBlazer!