There is actually not much information on this race, due the fact that it was terminated by Pitch, leaving Bunnymund as the lone survivor of his whole race.
What is known of them is what we actually see from Aster. They were a giant rabbit-kind people (6-7ft tall), who protected the planets, looking over their health and well being. They were also known as great warriors.
Part of pooka's powers were also to stop time travelers to go back in time and mess with the timeline. Nobody wants a messed timeline.
Then from the book we also come to the conclusion that they are able to shape the planets and adding continents (Bunnymund did this to Earth).
And then there is, the powers that are mostly seen with Bunnymund, and those are the martial arts experts and eating weird chocolate that expands their powers, and that work differently every time (I didn't understand this part) the fact is that at some point a pooka for combat can have like 3 pairs of arms (Creepy) or grow up even more, becoming enormous.
Pitch admits, that he almost lost in the battle against them, but then he won
and killed them all, well almost, Bunnymund survived.