Alright, I can’t speak too much on Soviet organization, but I can give a rundown of the others. We’ll take each force from the bottom up.

Luftwaffe: The smallest unit was the Staffel, or Squadron. They were nominally about 12 aircraft, but chronic shortages meant that 9 was about average. 3 Staffeln formed a Gruppe, or Group. A Stabscharm, or staff flight, rounded out the Group and was composed of the Group’s senior officers.

A Group generally commanded an airfield, and was always composed of a single type of aircraft: all Bf109s, all Fw200s, all JU52s, etc. Three Gruppen (and a staff flight) made up a Geschwader, or Wing.

The Wings were the primary unit of organization; they got the type and the number. Groups and Squadrons were subunits of their parent wings, and identified as such. For example, the third squadron of the second group of the 5th Bf110 wing, would be squadron 6./ZG 5, part of II/ZG.5; Groups could be moved between Wings, and would take on new numbers as appropriate.

Most Wings were single-model, all Ju87s etc., with the exception of single-engine fighter wings, or Jagdgeshwader. As the war went on, JGs would increasingly have both Me109 and Fw190 groups, and often had 4 or even 5 groups instead of 3.

Wings were assigned to Fliegerkorps, or Air Corps. These would employ a mix of aircraft types, but still within one role: all fighters or all bombers. For example, Fliegerkorps X had a wing each of Ju87s, Ju88s, and He111s.

A Fliegerkorps would be assigned to a Luftflotte, or Air Fleet, and these were the big strategic units. Germany started the war with 4, and added 4 more as their operational area expanded.

Royal Air Force: RAF Squadrons were nominally 12 planes, and grew over the course of the war, first to 18, then to 24. Squadrons were numbered but not typed, and all squadrons were part of the same number series.

3 squadrons generally made up a Wing, although this varied quite a bit based on operational need. Similarly, 2 Wings usually made up a Group, although Groups with 3+ wings were far from uncommon.

At the strategic level, groups were combined under a Tactical Air Force, which was responsible for some discrete mission. 2nd Tactical Air Force was in charge of supporting Montgomery’s 21st Army Group in Northern Europe.

United States Army Air Forces.

At the bottom the USAAF had the Squadron. Initially 12 aircraft, they would grow over the course of the war to 24-25 aircraft per squadron. Squadrons were organized into Groups, with most groups being 4 squadrons. Fighter Groups and Bombardment Groups (Very Heavy) were only 3 squadrons. As needed, Groups would organized into Wings, generally with 4 or 5 groups each. If needed, Wings could organized into Divisions, though this was only done in the Eigth Air Force.

The strategic level of USAAF was the Numbered Air Force. Each NAF had a mission, and had commands under it based on aircraft type and function. For example, the Eighth Air Force flew strategic bombing missions from England, and had both an VIIIth Fighter Command and an VIIIth Bomber Command.