If my son’s biological father has not seen or contacted us in over 4 years and hardly pays his ordered support, is there any way I can strip his parental rights?

Under the laws of all states in this country in order for the biological father to lose his parental rights as to his son, he must freely and voluntarily sign an adoption agreement with a third party giving up such parental rights subject to court approval on the matter. Unless the above can be done, you cannot "strip" the father of his parental rights as to your son.

There are a couple of ways you can accomplish what you are seeking.  The first is to try to terminate his parental rights completely.  Some courts hesitate to do this because it also deprives the child of the potential to collect child support or to inherit from a parent.  Your second option is to modify the custody orders and ask that the court not allow him to have any access to the child except at your discretion.  Your basis would be that since he has had no contact with the child in over four years that it would be emotionally difficult for the child to just let him "jump back into visitations." 

As far as movement is concerned, you can move to where ever is best for your child as long as there is not a restriction in your court orders.  If your custody orders contain a provision that you must reside within a certain county or state, then you would need to petition the court first before you move.  If you do not get the court's prior permission, then he could file an enforcement action against you later.  (Which probably wouldn't happen considering his historical disinterest).  If you do not have this clause in your orders, then you are free to move where ever and whenever you would like.