Orders of Battle – Reds
All orders of battle merely give a snapshot of the army at one point in time: and the Russian Civil War even more so than most wars. What lists we have tend to be associated with a reorganisation, so are much better evidence for the months following than for the months preceding them.
Note: different armies counted differently. The Whites tended to count only actual riflemen as "bayonets" and just line cavalry as "sabres", so not including any supporting troops. The Reds at first tended to count everyone in a rifle unit as a "bayonet", whether they had a rifle or not. It can therefore be inappropriate to just compare the straight figures directly.
Red Army
Some early war lists, showing the typical mix of units for the time.
11th Army (Caucasus), November 1918
Forces of Soviet Ukraine, late 1918
The forces facing Kolchak, the Orenburg Cossacks and Urals Cossacks in the middle of 1919.
The forces in Fergana, largely garrisons and fighting the emerging Basmachis. This was just before the collapse of Kolchak's forces, so was still the isolated forces of the region.
An orbat for those elements of the Soviet Southern Front at the crucial turning point of Denikin's drive on Moscow. Known as the Battle of Orel or, in Soviet literature, as the Orel-Kromy Operation:
Orel Strike Force, October 1919
The forces across the Don and Manych, February 1920
Caucasian Front, February 1920
The 1920 Polish War, from Гражданская Война В России: Война С Белополяками (Civil War in Russia: War with the White Poles) by Kakurin and Melikov.
Western and SouthWestern Fronts, 1920
An orbat for those units facing the White "Russian Army" in the Crimea above:
Soviets facing Wrangel October 1920
The units facing Yudenich during his drive on Petrograd.
Soviet 7th Army 11 October 1919, at the Start of Yudenich's Offensive
Soviet 7th and 15th Armies second half of the October 1919, in the critical period
Directives of the Red Army Command
This massive series includes, in Volume 4, orders of battle for the the entire Red Army at various times during the war. These have the added advantage that they were cross-checked and gaps filled where possible, so are probably the most reliable numbers for the Soviet armies.
Table 10: Formations and Numbers in the Forces of the Red Army, 21 July 1918
Table 18: Formations and Numbers in the Field Army of the Republic, 1 June 1919
Table 22: Formations and Numbers of the Red Army, in 30 August and 10 September 1919
Table 26: Formations and Numbers in the Field Army of the Republic, 1 November 1919
Table 29: Formations and Numbers in the Field Army of the Republic, 15 January to 15 February 1920
Table 34: Formations and Numbers at the Fronts in the Field Army, 15 May to 5 June 1920
Table 37: Formations and Numbers in the Field Army of the Republic, 1 to 15 July 1920
Table 40: Formations and Numbers in the Field Army, 15 October 1920
However it has much more than that, including other counts that aren't divided up by unit, naval and flotilla strengths, the forces of the Far Eastern Republic, and also Soviet estimates of the forces facing them over the course of the war.
Reference Material
A bit of a resource for tracking down Soviet Cavalry divisions: especially useful for when they changed names.
A resource listing all the major units of the Red Army composed mainly of foreigners.
The "Internationalist" units that lasted to the end of the war, with numbers.
Other Sources
The Trans-Dnepr Operation by Tom Hillman has good orbats in the back relating to the forces involved.
The Role of M.N. Tukhachevskii in the Suppression of the Kronstadt Rebellion by Neil Croll in Revolutionary Russia, Vol 17, No. 2, Dec 2004 is easily the best source of unit information on the Soviet side that I have seen.