After accidentally killing him and using his carcass to hide from Yumoto, Wombat must stay within range of Mr. Tawarayama in order to keep his lifeless body from rotting. Wombat can also control and to an extent communicate via it, and is often seen being carried underneath Tawarayama's arm, however has proven forgetful of staying close by -- this usually results in a decaying stench.
Earth Defense Club
Wombat is the one who prompted the five to become Battle Lovers against their will, much to their dismay and confusion. It seems able to control their speech and actions to a certain extent, which is displayed by the way that it made them say the "embarrassing" phrases before transforming (in certain earlier episodes, this was followed by protests).
Yumoto seems to be very infatuated with Wombat, as he extremely often engages in forced cuddle-sessions, much to the latter's chagrin, and tends to break out of the grasp on multiple occasions. This creates complications for the situation with Mr. Tawarayama, in which case Wombat has to struggle to escape and return life to the teacher.
Wombat was actually sent to fight the plan Hireashi was executing. He never told anything to the Battle Lovers and waited until the right time to reveal this piece of information (by accident).