In the early days of Soviet Power, a significant portion of their military power was from units of non-Russians, which are collectively lumped as "Internationalists". In practice they differed considerably in origin and military significance.
Because of the avowedly international outlook of the Bolsheviks, the internationalists were a major propaganda matter to them – they showed the other nations of the world were alongside the Communists in fighting the forces of reaction.
Some care needs to be taken then when reading material from the RCW period, as it often glosses over important distinctions. The Soviets regarded them all as "volunteers", which was often hopelessly optimistic, whereas the Whites tended to call them "mercenaries", which is just as wrong.
The Tsarist regime was opposed to any sort of nationalism outside of Russian nationalism, but in its last days started to allow units to form that were based on a non-Russian ethnic basis. These units were to prove far more resilient than the Russian ones in 1917 as the revolution took hold, and at the time of the Bolshevik Revolution provided the bulk of the cohesive units remaining combat capable.
The Czechoslovaks Legion was the largest – and most organised national army, at least politically. They were quite strongly Socialist in 1917, but the desire to fight the Central Powers and gain an independent Czechoslovakia took much greater importance in their eyes that the revolution. When the Bolsheviks prevented their transit to Allied territory they rebelled and kicked off the serious fighting of the Civil War. However their heart was never in the fight against Communism, and they soon withdrew from the front lines, in order to return to Europe.
Some Czechs and Slovak did fight for the Soviet cause. The 1st Penza Czechoslovak Revolutionary Regiment was one, and there were isolated battalions and companies. Care is needed though because many of such "regiments" and "battalions" turn out to be quite small in practice.
The Poles weren't as Socialist, and even if they were their primary allegiance was to an independent Poland. Their units resisted being surrendered to the Central Powers as the Treaty of Brest-Litovsk insisted and usually attempted to make it to Poland. Those that did fight as Polish units in the Civil War did so almost entirely on the White side (a division in Siberia, some near Odessa, a few in Murmansk).
The Soviets attempted to recruit a Polish Red Army to lead the invasion of Poland, but were largely unsuccessful. Most of those who were recruited were people of ethnic Polish background but who had grown up in Russia.
The Latvians and Estonians were treated as special cases. Unlike others, they were grouped into Divisions of largely only their own nationality and they remained viable forces into 1920. I have given them separate pages:
Russia had taken hundreds of thousands to POWs in WWI, especially from the Austro-Hungarian army during the Brusilov Offensive. They were generally sent to the interior of Russia, from where escape to their homeland was nearly impossible. When the revolution came the prisoners were released, but no other care was taken of them. In order to avoid starvation, many were forced to enlist in whatever the local army was to avoid starvation.
There were a large number of Hungarian POWs, especially in Siberia, and they were the group that most often fought willingly for the Red cause. However when Hungary declared a Soviet Republic, most of them hurried home to assist. Lenin allowed them to go, unlike the Czechs and Poles, in order to support the only other Communist state. So by the end of 1919 the Hungarians no longer made up many units in the Red Army.
Units made up mostly of Hungarians included:
The Serbians tended to prefer the Whites, and a division of them was formed in Siberia and evacuated through Vladivostok.
The Germans tended to stay aloof, and weren't particularly numerous, although a few fought for the Reds.
Quite a few Austrians fought for the Soviets, especially in Turkestan, but more out of necessity than conviction. Still, they were properly trained and disciplined, and while they didn't believe in the cause they were at least prepared to fight for each other.
There were a few Romanians and Yugoslavians, especially in the Odessa area, but the ability to easily move home generally proved too attractive for such units to last.
Workers had always moved around Imperial Russia, which is how ethnic Latvian regiments could be recruited in the Urals, as well as the more obvious Petrograd. But during WWI the empire suffered terrible manpower shortages and so imported large numbers of workers.
They proved to be excellent soldiers. They had no homes to desert to, and were largely entirely uninterested in revolutionary politics. This made Chinese and Koreans particularly useful for putting down internal revolts, and quite a few units of them were employed by the internal security forces for this reason.
Mostly they were placed as companies into normal units of the Red Army, though the 225th Rifle Regiment was Chinese.
Several units were made from Finnish Communists forced out after the attempted Communist take-over there failed and those living in Russia. Such units would probably have been extremely good, consisting largely of dedicated Communists. The 3rd Finnish Communist Regiment and 6th Finnish Rifle Regiment served briefly in Estonia, and then in Karelia, so not part of the main fronts. The 480th Finnish Regiment mostly served on the Karelian Front, and in Archangel, but did however fight in Poland in 1920.
POW Internationalists were not meant to wear their former uniforms but, since sometimes no other was supplied, they often did. If you are fielding an early war POW internationalist unit, then some of the old uniform mixed in is appropriate. (But they had been wearing those uniforms for quite some time, so units all kitted out like a WWI unit wasn't possible, and they were from a mix of units originally anyway.)
Otherwise they dressed like any other Red Army soldier, and there is a picture of the Latvians just before being sent to Orel that show them looking like a standard, if quite tidy, Red unit. For others, the Chinese shown in the Osprey C1 would be typical – down to the leggings and makeshift shoes.
Their flags seem to have been largely in their native languages. Certainly the Latvians were.
The uniform of the Red Hungarian Hussars is described in both the Osprey and AST books.
As the war went on, the Internationalist units started to fade. The pool of recruits was gone, many deserted in order to return to their homeland, especially if anywhere on the Western fronts. As the Red Army improved they lost their relative importance. There were only 15,000 to 18,000 registered in May 1919, most of whom would have been in the Latvian and Estonian divisions.
It can be hard to track them in the late war, as they tended to be merged into the regular army and be given standard numbers. The Soviets also started to dilute them with other nationalities, as they distrusted any separatist tendency. I suspect the Chinese and Koreans probably stayed the most separate, and the best.
A document listing all the "International" units for September 1920 only gives 5,000 men. While this is almost certainly not complete and excludes the Latvians, it does suggest that such units were no longer a major component of the Red Army. Noticeably they are mainly in the East.
The early war was the period when International units were a large portion of the Red Army, particularly in the Urals and Siberia. A small unit can be justified on almost any front at the time. They would generally be one of the best units in the Red Army.
Later war international units don't seem to have had quite the same elan of earlier ones, and were mostly included just as normal companies and battalions of the Red Army.
M.S. Kamensky. "The participation of the Chinese in the Urals Civil War: facts and memories"
Available from the Perm Historical Archives
"Foreign Prisoners of War in Turkestan 1917-18". Central Asian Review Vol. IX No 3. p 240-249.