This has been researched by butterzillion on freerepublic.com
The broad answer is that most things will stay the same. That is, if Congress voted for a law and BHO signed it, it will stand.
Vetos, however, may not stand.
Presidential appointments may not be valid. That is why Huber resigned as a BHO appointee and Trump reappointed him as a DJT appointee. Otherwise, all of the FBI/Justice perps could claim the signed indictments are fraudulent.
Executive Orders will probably be rendered null and void, unless DJT renews them.
Judicial appointments confirmed by the Senate (SCOTUS), etc. will remain.
Treaties not ratified by the Senate are null and Void (Paris).
There is a precedent in the law for handling an usurper in office. It is very complex, hewever, and would probably that a SCOTUS ruling to lay out the detail.