In the scene where Ophelia goes crazy and ultimately jumps out of the window, she sings "Hey non nony, nony, hey nony", which is a direct quote from Hamlet (IV/5).
The title "Do the Bard, Man" is a play on the song "Do the Bartman" and the fact that Shakespeare is also referred to as "the Bard".
The "Island of Sirens" song is a parody of "Copocabana" by Barry Manilow.
The Trojan War was actually chronicled in 'The Iliad' not 'The Odyssey,' which does not begin until after the war was over.
When Moe says "Greece is the word" it's a reference to the theme song from the movie Grease.