The man-children over at Street Rodder have added a second chapter to their attempt to guide you through the labyrinthine process of registering a vehicle whose body and frame may or may not be OEM. While their series primarily centers around performing the act in California, which is notoriously hardcore about registering specially-constructed cars, it can be done and has been done many, many times. Just make sure you don't install the stolen parts until after the CHP has made its inspection.
Street Rod Registration Part II [Street Rodder]
Register Your Rod...(Hopefully) [Internal]