Munch is a lonely Gabbit - a gentle frog-like creature who communicates with other members of its species through echolocation. Munch searches in vain for others of his kind: his entire race has been exterminated, since the Gabbit eggs ("gabbiar") is a delicacy, and their lungs have been used by the chain-smoking, powerful Glukkons to replace their own. The last of the Gabbits is captures by two Vykkers, owners of Vykkers Labs, where they conduct experiments on living creatures. The two implant a sonar device in Munch's head, concocting a plan to enslave him and use him to trap other animals. However, Munch discovers that the implant has given him new powers; using those, he begins to free the vicious Fuzzles, whom the Vykkers have been using in their laboratories, hoping to escape himself and help other creatures who suffer under the yoke of the Glukkons.

Munch's Oddysee is set in the fictional Oddworld universe; its events take place after those of Abe's Exoddus. The player controls Munch as well as Abe, the hero of the previous Oddworld games. Abe's abilities haven't changed much since the last installment: as before, GameSpeak must be used to communicate with other creatures, leading them to safety. His fellow Mudokons can now be ordered to attack enemies. Abe can also grab and toss Mudokons or Munch to lead them to area they cannot access otherwise. Possessing enemies also comes into play, and is needed to solve many of the puzzles. Possession abilities can now be used to ignite quarrels between enemies and make them fight each other.

The player can change between Abe and Munch instantly throughout most of the game. Munch brings on the table new abilities of his own: he can use his sonar to control or immobilize specific creatures, as well as swim. Another new addition is the possibility to use vending machines, which sell various items that enhance the abilities of the protagonists. At certain points Abe and Munch can also remote-control mechanical creatures.