For Orders of Battle (i.e., what units were present during a particular battle), this site is outstanding:
Nafziger orders of battle collection : finding aid.
http://cgsc.contentdm.oclc.org/cdm/s...coll11/id/1277
This site is nothing but historical Orders of Battle - some of which are quite detailed. If you get lucky, you get great tactical scenario design info like number and types of weapons assigned to a particular unit.
The other digital resources in the CARL collection might also be useful, but I haven't had a chance to explore them yet.
Searching by specific unit will usually bring up useful information. There are WW2 aircraft and Axis history forums which often have useful threads by area specialists. Given the obsessive and nit-picking nature of historians and war game geeks, if there are errors in these threads, they're at least errors that reflect the current conventional wisdom!
Archive.org often has useful web pages which have otherwise been lost. That's good for chasing down links which otherwise return "404" or "This domain is for sale" results.
Many Air Forces maintain official history sections, as do many National Archive sites. They're good for (mostly) accurate if incomplete summaries of things like unit histories and equipment.
The real trick is discovering exactly which model of aircraft a unit was using, exact unit strengths (especially planes available vs. official strength), supply condition, and pilot quality. For example, it's easy to discover that, say, JG 1 was involved in the Battle of Britain, and that it was equipped with Bf-109s, but a pain in the ass to discover little gems like, "mostly still equipped with Bf-109E-1 as a of July 1940, 1 Staffel equipped with Bf-109E-4", "pilots mostly veterans of the Polish and French campaigns, with a few with experience in the Spanish Civil War", or "just 15 planes flyable on July 15".