What are the most important themes in The Odyssey?
I think one of the most important themes in The Odyssey is responsibility. If you take a look at Odysseus, he exhibits it and tries to demand it of his men.
Another would be loyalty. Both Penelope and Telamachus had to have borne much discouragement from the suitors and townspeople for waiting so long for Odysseus. Odysseus himself was working hard to get home, but his loyalty could be questioned even though he said of the goddesses that in his heart he never gave consent.
You could say self-identity is a theme as Odysseus reclaimed his rightful place and held fast to his role as king, defender and soldier.
Finally, you might consider choice and consequences. Many characters in this story reap trouble for sowing trouble and triumph for hard work.