The big ones are easy to cover. In a nut shell, The Marine Mammal act of '72 makes it illegal for non-natives to buy sell trade or barter any marine mammal part that was harvested after 1972.
If you buy materials from marine mammals, like walrus ivory you have to make sure the animal died before 1972.
Whale parts also have other rules regarding interstate commerce, whale bone may not be traded accross state lines. You may buy whale bone in person and bring it home but you may not order it from accross state lines. Sea cow bone is getting more scrutiny because wildlife officials believe that whale bone is being sold as sea cow bone because it has less restrictions.
For these reasons, when I buy walrus ivory that I am not sure is ancient (what we call "fossil") I make sure to get documentation to help show the animal died before 1972. I do the same for elephant ivory, the date for that is '89.
The documentation is as simple as a statement from the people you bought it from that says where the material came from the date it was obtained, a detailed discription of the material and the contact info of the person you bought it from, it is signed and dated. A picture of it in a den with old furniture and hair-doos around is better. When I make a knife or sell the material to another person, I make a copy of the document, add a note that says what I did. You can't fake this things, it has to be the real deal.
Antler and horn also have regs but they are different from state to state.
Stay safe and don't get into trouble just because you want to use sone cool material.