He should be able to move back into the home providing there is no separation agreement stating that the home belongs to her. Since he is still paying the mortgage and utilities then I would find it’s safe to say they have no agreement.
He can file for equitable distribution to get 1/2 the furnishings back but the other marital assets will also need to be divided then also. Since there are older children involved, I suggest that they do not allow her to remove all of the items from the home.
Normally, there is no age at which a child can choose who they live with but given the ages the 19 year old is legally an adult and can choose regardless. The 16 year old would probably not be forced by a judge to live with a parent that he did not want to live with.
He really should consult an attorney and get a separation agreement drawn up…