Not Mainly about Homer's Odyssey?
3 sinners (Everett, Delmar & Pete) on a quest for salvation, pursued by the devil. Opens with a chant in which "Po Lazarus" (biblical, referring either to a man condemned to hell, or a man resurrected by Jesus, or both) is being pursued by the sheriff; thereby equating the lawmen with the powers of Hell. Then, as the three sinners flee the chain gang, the sound-track plays "The Big Rock Candy Mountain", representing a sinner's, warped and humorous vision of paradise. They try to escape on the train but Everett's pride, and failure to help his fellows, holds them back.
They then meet a blind seer, who tells them that they will find a treasure, but it will not be the treasure they seek; that they will see marvels, such as a cow on the roof of a cotton house; that they are not to mind the twists and turns; nor the obstacles in their path, for their ultimate goal will be their "salvation". They debate what he means, and Everett dismisses him as an "ignorant old man".
The sheriff catches up with them at Pete's cousin's barn and we see hellfire burning in his eyes. After escaping, they meet a Christian congregation, singing the baptismal hymn "Down in the River to Pray". Pete & Delmar get baptised, but Everett mocks them as "ignorant fools" believing in an "ridiculous superstition". In an ironic foreshadowing, he says "even if it did put you square with the Lord, the state of Mississippi is a little more hard nosed". Pete retorts that baptism, at the very least would wash away "the stink of that pomade"; which turns out to be a good point, because it is by the pomade and hairnets (representing Everett's pride and vanity) that the devil/sheriff is tracking them.
They pick up Tommy, who has just sold his soul to the devil (at a crossroads -- the traditional meeting-place). Everett treats it as a joke, but Delmar is shocked. Pete asks what the devil looks like, and Tommy says "white as you folks...with empty eyes and a big hollow voice ... travel around with a mean old hound dog" (matching the sheriff). At Tommy's suggestion, they stop and play a song for the Blind Radioman. Everett introduces himself as "Jordan Rivers" (after the Jordan River, traditional baptismal site, & symbolically, border river of God's promised land); and his fellows as "The Soggy Bottom Boys" (a reference to their baptism), and that they sing "songs of salvation". They sing "Man of Constant Sorrow" ("... There is one promise that is given; I'll meet you on God's golden shore").
That night Tommy sings a song about hard times, with "people drifting" who "can't find heaven". The devil/sheriff shows up, and Tommy (terrified, evidently, that the devil has come for his due) flees without waiting for his fellows. Everett, obsessed with his pomade and hairnets, almost gets himself caught, but Delmar and Pete dissuade him. Eerie music plays while a man with a hound dog is silhouetted against the hellfire of the burning barn. We next get a travel montage while the soundtrack plays "…from these prison walls I'll fly ... Hallellujia ... to a land where joys will never end"; and as this plays, our escaped heroes hide from a prison-truck rolling by.
They next meet the Sirens, who are agents of the devil ("you and me and the devil makes three"). The Sirens drug Everett & Delmar, truss up Pete, and deliver him to the sheriff/devil. Everett & Delmar, however, wake before they can return. They then meet the robber Dan Teague (Cyclops) who reminds us that not all who claim to serve the Lord are what they appear. Next comes a horrific scene of poor Pete being tortured by the powers of Hell; the Lawman with the Hound shows up, and Pete is in awe and horror as flames again burn in his eyes. Pete is about to be hanged. Thunder rolls and the devil remarks "sweet summer rain, like God's own mercy". A noose gets thrown up and the devil remarks "stairway to heaven; we shall all meet by and by". Pete calls on God's forgiveness, and the devil says "Hold!" (his power has limits).
Next, at the Homer Stokes campaign, we see three adorable little "Wharvey Gals" singing "In the Highways" in harmony ("... I'll be somewhere, working for my Lord..."). Later as Everett bemoans the inconstancy of his wife to Pete & Delmar, they see Tommy about to be lynched by the KKK. During the rescue, Tommy objects "I don't think nothings going to save me; the devil has come to collect his due"). Everett's hair gel once more betrays him to the Powers of Hell, and Dan Teague/Cyclops sniffs him out.
The quartet make their getaway (temporarily) and get pardoned by the governor of Mississippi. Thinking the pardon makes them safe, the 4 head for the valley to retrieve Penny's wedding ring, only to once again get caught by the sheriff/devil (who says, depending on how you choose to hear it, either "You have eluded fate an' you have eluded me..." or "you have eluded Satan -- you have eluded me..."). They object that they have been pardoned by the governor, but the devil tells them "the law is a HUMAN institution" (he, the devil, is not bound). Thus is Everett's mockery of the power of baptism (the state of Mississippi is NOT more hard-nosed after all) turned on its head. Everett prays for forgiveness ("Oh Lord, please look down and recognize this poor sinner ... I know that I have been guilty of pride and sharp dealing ... I'm sorry that I turned my back on you...") and the 4 get saved by a giant baptism, which not only miraculously unties the devil's bonds, but washes away (among other things) an entire supply of Dapper Dan pomade.
Once he surfaces, Everett immediately turns his back on God again, and argues for a "rational explanation" (they knew the valley was going to be flooded); but is immediately silenced when he sees a cow floating on the roof of a cotton house, reminding him of the words of the blind seer. In the final scene, the "Wharvey Gals" sing another hymn ("my strongest trials now are past; my triumph has begun ... O bear my heart to him who bled and died for me, whose blood now cleanses from all sin, and gives me victory ..."), but in which Everett (having again turned his back on God) learns that his trials are not quite past, and he must again return to the river. As Everett objects that what Penny asks of him is "one hell of a heroic task", the blind seer rolls by on his railcart, finishing the hymn (..."oh bear me away on your snow-white wings, to my immortal home"). Perhaps we are reminded of his prior words: ("do not mind the obstacles in your path, for fate has vouchsafed your reward"). The same hymn ("angel band") is reprised as the credits start rolling.