The Odyssey Narrator:
Third Person (Omniscient). Mostly.
Our poet (might as well call him Homer) shows us everything that happens in the Odyssey—gods and mortals; good guys and bad guys; father and son. There's a reason they call it epic.
There is the little matter of Homer's invocation to the Muse in Book I in which he uses personal pronouns and refers to himself as telling the story. But the invocation to the muse is a standard part of epics; it's not really meant to introduce Homer as a character. Instead, what we have is a third person story focused around either Odysseus or Telemachos.
In Books IX—XII, Odysseus steps forward and becomes a first-person narrator. This is cool for two reasons: (1) We get to see how he views his experiences, whether he's learned from them, and whether he still suffers from certain key flaws, like (cough) excessive pride. (Check out Odysseus's "Character Analysis" for all about everyone's favorite Greek hero.) And (2) we start off in the middle of the story, with all the excitement of wondering how Odysseus will deal with the suitors without having to watch him suffer through years and years of misfortune.