If my ex-husband and I both live in the same state but he has custody of our 2 children, can he move out of state without my consent?

It depends on if there is a court order or not.  If there is a court order--then generally speaking, he would need to go to court and request the court's permission to move away with the kids.  This "move away" type of case can be very complicated, even for seasoned family law attorneys.  The bad news for you is that under Family Code 7501 and a series of cases (LaMusga following IRMO Burgess) have stated that the primary custodial parent has a right to move away with the children--and the burden of proof would be on the non-custodial parent to show that such a move is detrimental to the children.