The oldest source of law in the US is?

British Common Law. Many of the laws come from case law that has been published. In theory if there is no statute and you can find a relevant case that goes back to the Middle Ages you can cite that in your case and win. There have been cases from the 1600's cited to establish precedent and strengthen your arguments.

As far as the oldest statutory law in the United States it's the Mayflower Compact.