Other than "Dirka, Dirka Mohammed Jihad," there is nothing in the lyrics that is unmistakably and unquestionably a reference to TEAM AMERICA: WORLD POLICE. That is, there is no Iraqi girlfriend or a moment in the film where a member of Team America shoots from behind a TV after using a young girl as a human shield. But it is a running joke throughout the film that Team America is a bit ... careless ... about collateral damage.
The film's first scene is a raid on Paris which kills some terrorists but which destroys the Arc de Triomphe and the Eiffel Tower in the process. The specific line "Dirka, Dirka, Mohammed Jihad" comes during a scene in which one of the commandos tries to infiltrate a Cairo cafe where The Terrorists are meeting; saying that gets the Val Kilmer-like character into the meeting. That scenes ends with much blood being spilled in as gory a way as puppetry allows, plus the destruction of the Sphinx and the Pyramids.
It wouldn't surprise me that TEAM AMERICA: WORLD POLICE is a big favorite among our uniformed men. It's one of the few movies of recent years that mocks Michael Moore, Susan Sarandon, etc., has a real-life bad-guy unmistakably identified as such (Kim Jong-il) and ends up being unabashedly jingoistic about the need to kick ass, even if you do so imperfectly on occasion. The closing soliloquy about "assholes, dicks and pussies" puts it all in a nutshell in the first quote here. It's rather ungenteel (this is Trey Parker and Matt Stone, remember), but then the Marines are too. And the whole point -- the closing soliloquy, the movie, Josh Belle's song -- is that the warrior virtues are not to be judged by the shrinking-violet lace-curtain values of the Cambridge-Hollywood Axis.
One thing I didn't mention to Stacy: It's also clear to anyone who knows anything about the history of war songs and war stories that soldiers have always engaged in gallows humor and sick jokes, partly from "brutalization" (not a bad thing within limits, BTW; we want warriors to be "harder" than civilians) but also partly as a way of dealing with the constantly-made-imminent fact of the men's own mortality. At the very start of Western civilization, Homer tells dry jokes about how some soldiers "have the black fog decend upon them," including one sequence in THE ILIAD where he compares a Trojan being speared through the jaw to a fish trapped on a hook. Nor is this confined to soldiering; all professions have humor, within the stakes of that profession. I have never worked in a newsroom where you couldn't get at least a knowing smirk with a reference to lines from Don Henley's "Dirty Laundry" ("The boys in the newsroom got a running bet: / 'Get the widow on the set / We need dirty laundry'.") In a boxing movie called THE SETUP, all the "red corner" fighters share a single dressing room, and one guy who's just won his fight is telling everyone else in graphic detail about how he worked over his opponent, mercilessly punishing his "soft" stomach and ribs. A green young lad getting ready for his first fight has to flee the room to throw up, causing the victorious fighter to ask in a puzzled manner: "what's the matter with him." Sick humor in a life-and-death situation is simply letting off steam; there have never been soldiers in any war who haven't done exactly the same thing, only ouytside the glare of scrutiny by the Cambridge-Hollywood Axis.