• the overwhelming happiness brought by the lotus.
• OBWAT: Pete and Delmar (the crew) repent for their sins via the river baptism, happily forgetting their duties.

Sirens

• TO: Odysseus clogs his crew's ears with wax and has himself bound, so that only Odysseus may hear, but not act upon, the seductive sirens' cry—or song.
• OBWAT: The main characters are accosted and seduced by three singing women alongside the river. (BONUS: when the men awake, Pete seems to have been turned into a "horny toad," a parallel to how Circe turns Odysseus's men into animals.)

One strong parallel between The Odyssey and the movie O Brother Where Art Thou is the blind railroad man who tells the three runaways their future (they will see a...a cow on the roof of a cotton house). In the Odyssey, Odysseus meets Tireseus from the underworld, also a blind man who tells him his future. 

In O Brother Where Art Thou, the three men (Pete, Delmar, and Everett) meet three women who get them drunk and take Pete back to prison for money. In The Odyssey, Odysseus runs into the three sirens, beautiful women who sing and cause him to become confused. (In the movie, their song is "Go to sleep you little baby..."). 

Both Everett and Odysseus are trying to return to their families after an extended amount of time apart. Everett was in prison, however, Odysseus was nobly serving in the war. However, one difference between the two is Odysseus is a very physical, strong man while Everett is not as much physical as he is intelligent. However, when it comes down to it, they are both just men--compared to stories where the main character is some sort of demi-god (Hercules).

In the movie, Everett and Delmar meet Big Man Teague who effectively robs them under the pretense of wanting to begin a business arrangement with them. Big Man Teague also has an eye patch over one eye, causing him to look somewhat like a cyclops. Similarly, Odysseus has to run away from the brute of a cyclops--the difference here being that the cyclops is purely out for a physical destruction of Odysseus--Teague doesn't care if he physically destroys Everett and Delmar, but he cares about the financial side of it. 

To the extent that there are similarities between Homer’s epic story The Odyssey and Joel and Ethan Coen’s 2000 film “O, Brother, Where Art Thou?” this is no coincidence.  While the genesis of the story of escaped prisoners encountering all-manner of adventures on their quest to return home was not consciously based upon The Odyssey, the brothers recognized the similarities in plots and adapted their screenplay accordingly.   The following quote from an interview the Coens did provides the background:

“We didn’t really start with Homer,” Joel explains.  “We started with the idea of these three fugitives escaping from the chain gang and Homer suggested itself later when we realized the movie was essentially about the main character trying to get home and having this series of adventures along the way.”  At this point they remember this old Greek writer called Home.  “We never actually read it,” Ethan interjects.  “But we read the comic book version of The Odyssey and tarted the movie up with the Cyclops, etc.” [www.darkhorizons.com/features/217/o-brother-where-art-thou]

Once the decision was made to expand the parallels with The Odyssey, the Coens made the requisite adjustments in their screenplay, starting with the name of the lead character, Ulysses Everett McGill, “Ulysses,” of course, being the Latin name of the war hero Odysseus whose adventures during his long trek home following the Trojan War is the protagonist of Homer’s story.  The similarities go way beyond the protagonist’s name, however, as suggested by the Coens in the above referenced interview.  Characters and events that occur throughout the film have parallels in The Odyssey.  Just as Odysseus’ grown son, Telemachus, believes his father to be dead, a casualty of war, so do Ulysses Everett McGill’s daughters believe their father to have perished or, to be more precise, to have been “ran over by a train.”  Similarly, Odysseus’ presumed “widow,” Penelope, has her parallel in McGill’s “widow,” Penny [Penelope-Penny, get it?].  Both women have suitors, all believing the husband to be deceased, but Penny’s suitor is considerably more attractive an option than Penelope’s army of would-be suitors.  The film’s character of Big Dan Teague represents Homer’s mythical Cyclops, the one-eyed giant and shephard that devours humans that cross its path.  Big Dan similarly has only one eye, works as a shepherd, and has a voracious appetite: “I’m a man of large appetite, and even with lunch under my belt, I was feelin’ a mite puckish.”

Other similarities or parallels abound.  Just as Odysseus disguises himself as a homeless beggar in order to observe his wife and her surroundings, so does “Ulysses” McGill disguise himself as a homeless beggar to secretly observe Penny.  The God of the Seas, Poseidon, torments Odysseus throughout his journey; the prison warden tracks McGill throughout his.  There are more such parallels, but this should provide the basis for further discussion.

O Brother Where Art Thou? has several allusions to The Odyssey in its narrative, themes, and characters.

Firstly, the George Clooney character, Ulysses, is based directly on Odysseus. (Ulysses is the Latin variation of the name Odysseus, which is important to keep in mind.) Like Odysseus, he yearns to return home and reunite with his wife (called Penny instead of Penelope in this story). He undergoes a journey wherein he meets strange and menacing figures who want to prevent him from achieving his goal for a variety of reasons.

Several characters in the film reference corresponding figures in Homer. The blind prophet Tiresias is replaced with an old blind man on the railway who also tells future events to the protagonist and his companions. The sirens are replaced with three shapely wash-women who drug the men with liquor. The KKK become a stand-in for the Cyclops, with the main characters disguising themselves as clansmen the same way Odysseus and his men used sheep's wool to disguise themselves during their escape.

And so on it goes. Though the plot isn't exactly the same as The Odyssey, the movie riffs a lot on the epic poem.