I moved to Colorado in July 2009 with my four children. I moved in with a boyfriend and left my home and job in another state. Now I am trying to move but I want to know if he can just kick us out

If you are a resident then he can't just kick you out. He has to follow the procedure for evicting a tenant even if you don't pay any rent. That means he has to give you written notice that your tenancy is terminated and he has to file a lawsuit for eviction if you don't move out at the end of the notice period.

If he tries to kick you out then call the police.