Can a teenager move in with family without parental consent? ?

It is illegal to "stay" with anyone without the consent of your custodial parent.

It depends on how old the teen is. In a civilized nation it would be for all teens. 

Some custody agreements might be loosey goosey enough for a kid to go back and forth at will (and I knew a kid with this arrangement when I was in high school). But generally they dictate down to the minute when and how much time the child must spend with each parent. Ultimately it would come down the parent(s) allowing it because in most cases they'd be entitled to report it to the police as custodial interference (or even kidnapping). 

Strictly by the letter of the law, a minor can't walk out the door without parental consent.

In a joint custody case, the custody order doesn't give the CHILD an option.

It is legal to stay with either parent if they are separated unless there is a specific court order saying otherwise. You can not stay with anyone other than your parents without a court order or their consent. 

There is NO "other custodian".. If your parents are separated, ONE is the custodial parent.

No, you cant just go move somewhere without parental consent

Only if they are 18 or over.