How long can he keep coming here and removing items that he says are his?

Until someone files a complaint and requests an order barring the transfer of marital property, either in the complaint or in a motion. Even then, if he takes property, you have to go to court to enforce it. You may want to just keep track of everything you can, photo it and look for the receipts so when the court goes to divide your property, you have a record of how much value of the marital estate he took.