My guess as regards an air force is probably not. It seems difficult to imagine why something like that wouldn't have been mentioned in the game. We only ever see two aircraft used by NCR, the president's vertibird and a vertibird at Long 15. Given that vertibirds were generally considered to have been post-War enclave at the time of NV, these are fairly recent acquisitions for the NCR. My guess is that up until recently, there just wasn't all that much utility in really investing with airplanes to a great degree since they didn't really face any armies fearsome enough to warrant it. They probably have them, they use them for reconnaissance and such, but they don't devote much resource to them.
To navy - probably not just because there doesn't seem to be anyone to trade overseas with, and it doesn't seem like there would be any threats coming to them from the sea. Maybe there's raiders or BoS out on the Channel Islands but probably not.
Almost all major ports, harbor, shipyards and naval bases would have been nuked, those are pretty early on the list. And a huge portion of the military fleet would have been overseas to fight the war. For those that remained home, along with whatever civilian fleet - well I don't think being left unattended for a 150 years bodes terribly well for a ship's seaworthiness. Most of them sunk, most of the remainder were probably broken down for scrap. Things like the Valdez are the rare exception, not the rule.
Real Caligula Hours in Shady Sands