What is the role of gods in Homer's Odyssey?
This is a good question. The gods do not act in any one particular way in Homer's Odyssey. A few examples should make this clear.
First, when Telemachus is about to visit Nestor at Pylos in book two, Athena appears to him as disguised as Mentor. She encourages him to go and gives him the help that he needs. Telemachus actually needs this, because he is young and insecure.
Second, in book nine, Odysseus recounts to the Phaeacians that while he was at sea, Zeus sent a storm and buffeted his men for nine days and sent them to the island of the Lotus-eaters. Odysseus escapes only to find his way to the island of the Cyclopes, where he blinds Polyphemus to gain the ire of Poseidon, who is the father of Polyphemus.
Finally, Odysseus is able to make it home to Ithaca, because of the constant help of Athena. And when Odysseus kills all the suitors, Athena makes the fathers of the suitors and those who want revenge to forget about their loss.
In light of these example, we can say that the gods intervene in the lives of men in many different ways.