This has alot of stuff. Everything except the air force is mainly from the 1960s onwards, but the air force section covers the 1950s fully. It doesn't give numbers of aircraft, but the number of aircraft in a fighter regiment according to Wikipedia is 40-42 (if someone has a more accurate number, feel free to correct me).
For non-Soviet OOBs, I search the aircraft I am looking for on Wikipedia, and go to the "users and operators" section (or whatever it is called). Most of the time, there is a listing of the squadrons that operated it, on the pages for the squadrons it will have their bases and their parent units/formations. I just use generic numbers though. It isn't the most efficient. Someone else probably knows of dedicated websites for Cold War OOBs for different nations but I don't know of any.
You mentioned F-84s, so I am not sure if "Peeling the Onion, 1957" that boogabooga mentioned will necessarily be what you are looking for, however, even if it isn't, not only do I recommend that you play it because it is a good scenario, but also, playing it will give you an idea of the different potential design aspects of a nuclear war scenario.
Formerly known as Project2035, TyeeBanzai, and FlyForLenin