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.
The entire Polish Army in August 1920, at the time of the Battle of Warsaw. It includes the numbers for most of the divisions, taken from Sikorski:
Battle of Warsaw orbat in pdf
The 5th Army, north of the Warsaw bridgehead, down to battalion, squadron and battery level:
Polish Fifth Army mid August 1920 in pdf
The 1st Army, defending the Warsaw bridgehead, down to battalion, squadron and battery level, along with organisational charts and some notes, taken from Waligóra's Battle for the Outskirts of Warsaw, August 1920:
Polish First Army 15 August 1920 in pdf
For the Battle of Komarów (also known as Cześniki) see my article in the history section:
Wikipedia has an order of battle
Again we have the 1st Army in more detail, this time down to regiment level:
Polish 1st Army at the Nemen in pdf
The original in Polish in pdf
Some individual units fighting in the southern part of the Polish forces, facing Budenny:
Polish 7th Infantry Division in August 1920 in pdf
Polish 18th Infantry Division in July 1920 in pdf
Later in that same theatre, just before the war ended.
The Estonian Army at the peak of the Drive on Petrograd.
An orbat for the brief attack near Mozyr' by the Russian Peoples' Volunteer Army under the command of Bulak-Balakhovich:
NDA orbat in pdf
There is an orbat for the Galician Ukrainians, who largely fought the Poles at this time:
UGA early 1919 in pdf
The design notes for the board game Tachanka! have a useful list of Makhno's units, as he moved between Nationalist and Red Army factions.
Latvia 1919 has some.
How Odessa Became Red has some numbers for the French and Greek forces involved in the Odessa campaign.