It's actually pretty simple, and people do it all the time.
You'll have to get the cars inspected (most gas stations can do this), then you handle the car registration at the county tax assessor's office (rather than the DMV). Bring the inspection certificate, proof of car insurance, and proof you own the vehicle -- your CA registration certificate will do.
You won't have to change your existing loans, but be sure and let the loan holder know the car is now located somewhere new.
Texas DMV - What to do when you move to TX