Hmmm I wonder what the oldest statute is
The very first act passed by Congress under the Constitution, concerning the administration of oaths of office for various offices, is still on the books, codified in the U.S. Code in various places depending upon the office. I doubt if any statues are on the books from the Confederation, tho I suppose it would be possible for a land title case in the old Northwest or Southwest Territories to make use of such an old law.
The supposed reason that Texas can't secede is because the AOC created a perpetual Union and the Constitution made it a more perfect Union.