O Brother Where Art Thou is obviously based on the Odyssey, and there are multiple parallels and allusions to the Odyssey in O Brother Where Art Thou. Everett, of course, is a stand-in for Odysseus. Pete and Delmar are his (often inept and disobedient) crew, the three ladies are the sirens, the KKK member is the cyclops, etc. etc. However, I think it's a good idea to consider that Pete and Delmar aren't just representations of Odysseus's crew.
First off, Everett isn't a very Odysseus-like character. Sure, he's the dubious hero, and he's cunning and wily, but he doesn't have all of Odysseus's traits. Most of that can be attributed to the fact that O Brother Where Art Thou is not an exact copy of the Odyssey, so the characters will differ. But also, maybe Everett isn't entirely Odyssian because he's only one third of the Odysseus figure in O Brother Where Art Thou.
Pete and Delmar represent the other two thirds of the Odysseus figure in O Brother Where Art Thou. Pete is Odysseus's loyalty to his crew and family. Even though his cousin sells them out for the bounty on their heads, Pete still gets mad when Everett reveals that he stole Wash's watch. Pete doesn't seem to care about the fact that Walsh betrayed them.
Delmar represents the part of Odysseus that respects and fears the supernatural. Delmar is superstitious and eager to believe in a higher power. He immediately believes that Pete has been turned into a toad, and he is the first to be baptized. He puts more stock into the supernatural than Everett and Pete combined. Everett, of course, is skeptical of anything dealing with a higher power, and believes that everything can be explained by science.
Everett is the most Odyssian of all the characters, and he is (of course) the hero. He, like Odysseus, is a clever and cunning man. He has Odysseus's slightly amoral personality, and his charisma. He's the one on the quest to get back home, and he drags the others into it with him.
