There are a lot of songs that relate directly to the epic, either by retelling parts of it, or using similar themes to describe other events. Here are a few:
"Tales of Brave Ulysses" (Cream) -recounts Odysseus's encounter with the Sirens
"Home at Last" (Steely Dan) -also inspired by the Sirens story
"Ulysses" (Franz Ferdinand) -loosely based on the Odyssey (Ulysses is Odysseus' Latin name)
"Wrapped Around Your Finger" (The Police) -opening lines mention 2 monsters from the poem
"Home by the Sea" (Genesis) -also based on the Odyssey
Many more songs have a general theme of returning home after a long journey, which is a theme that pretty much started with Homer. These are everywhere.
Hope this helps! (also you may want to see if other people have asked the same question on Yahoo! already- it'll save you some time.)
Calypso by Suzanne Vega is sung from Calypsos point of view just after Ulysses (Odyseus) leaves her island after several years
i think that the best ways to search for songs would be to look at the themes of odyssey.
themes such as:
...The Power of Cunning over Strength
...the Pitfalls of Temptation
these are some symbols:
The Wedding Bed
i hope this helps!