He may be irate, but his company has to pay you for the days you worked, and he said it will. Most states allow terminating employees to be paid on a normal schedule; a few require faster payment, but even if you are in one of those states, I wouldn't bother making a case out of that as it will come back to haunt you should he ever have to give a reference for you. (And 99 out of 100, someday he will.)
The vacation pay is a different matter. If it is vested, and you can prove it, the company should pay you for it. If however the rules are unclear, it may not be vested. For example, the rules may say it can be taken at the end of one year, or if not taken within the year it is lost. So I suggest you carefully look at the manual and explain it to the boss nicely, by phone and then if needed, in writing, and if he doesn't give you satisfaction, ask his management for satisfaction.
