I have known a fairly different version to these most of my life. I grew up in mid-Westchester County, NY. This was a sort of bus-trip song in the late 60s and early 70s, as in on field trips or to events, and it was evidently just a fragment of the songs many of you have remembered. It would just go round and round the verse and be repeated.

No Lenin, no Trotsky, no Russian diplomatsky
Can stop us in our plotsky to overthrow the czar [yes, I know that doesn't make sense, I'm just reporting what I remember was sung]
When comes the revolution, we will find solution
And you will all see red
Hey!
Aye-yi-yi-yikus
Nobody like us
We are the ones from [insert town name]
No Lenin, no Trotsky, no Russian diplomatsky... etc.

So funny that a song that probably came out of some Workmen's Circle camp found itself sung as a suburban American school-spirit fight song, not even remembering which side was which. Don't shoot the messenger.