As a clarification to the Odyssey connection of this film: it was never intended to be based on Homer's Odyssey. Hell, the Coen Brothers admit to having never read it. Rather, they realized they were making a movie about a journey and thought it would be neat to bring in more elements from Homer (which they thought was a cool hillbilly name, and nothing more).
So, they watched the 1954 Italian film Ulysses and bought the Odyssey comic book and did a little research on the cyclops and Penelope and sirens. And, kiddies, that's where the Odyssey connection comes in. Nothing more than "hey, that's a neat idea."
Or so they say.