davyr, wasn't that "The thing that I bury..."? or possibly "The ghoul that I bury..."? I think the parody was called "Manny get your ghoul".
Memories have faded as regards the West Side Story parody - possibly it was called "East Side Story" (is the U. N. building located on New York's East Side?) I remember a song sung by Mao Tse Tung (I think that's how his name was transliterated back then), which included the lines "Please be sweet to us, and give a seat to us. [????] and such joy you'll get, like we gave Tibet" and later there was a verse that ended "like our troops are in North Vietnam". Another section was "That's right! You bet! We will preserve law and order, like when we crossed India's border." All to the tune of "There's a Place for Us".