Most irregular galaxies are thought to have formed from nebulas that cooled very quickly right after the big bang from cosmic background radiation from collisions between other galaxies

Most irregular galaxies are thought to have formed from collisions between other galaxies.

This is just one wat that irregular galaxies are formed; the collision is due to the interaction of their gravitational forces. These galaxies might have been regular before the collision, but are not deformed. 
Another form of irregular galaxies are the ones that are still very young and therefore have not yet reached their symmetrical state.

From collisions between other galaxies.