"Ivan Meets G.I. Joe" started as a brief band in-joke from an interview guitarist Mick Jones had given to Rolling Stone
magazine, in which he concluded that "people prefer to dance than to fight wars." ("G.I. Joe" is a term for an American soldier, and also the brand of a popular military-themed line of toys, comics books, and even a movie franchise.)
In that regard, Joe Strummer's lyrics make perfect sense: they cast the two world superpowers involved in the Cold War into a disco dance competition, and turns their imposing chemical weapon threats into bizarre dance moves ("The Vostok Bomb, the Stalin strike, he tried every move, he tried to Hitch Hike
There are also brief mentions to The Clash's own favorite nightclub haunts such as New York's Studio 54 and Le Palace in Paris. The song ends on an ironic note where the spectators of the "dance-off" get bored with America and the USSR's posturing and go "Over the road, to watch China explode!"