What roles in Odysseus' life do the three most important gods play in Homer's Odyssey?
There are a number of important divinities in Homer's Odyssey, although sometimes we forget that some of them are divinities.
First, and most obviously, we must mention the goddess Athene. She serves as a constant supporter of Odysseus and his family. She inspires Telemachus to search for his father and she is at Odysseus' side when he battles against the suitors.
Second, we must recall the god Poseidon, who aligns himself against Odysseus after the hero blinds Poseidon's son in Odyssey 9.
As for which divinity we should assign third place, this is difficult to narrow down. On one hand, we could suggest the sun god Helios, who arranges to have Odysseus' last remaining ship and the rest of his crew destroyed.
Circe, who is also a female deity, could be included. She provides Odysseus with lots of advice and guidance about how to avoid various obstacles on his way back to Ithaca.
We could also mention Zeus. After all, he is king of gods and men and he does set in motion Odysseus' departure from Calypso's island.
Speaking of Calypso, we cannot forget that she, too, is divine. Seven of the ten years that Odysseus spends wandering the world after the fall of Troy are spent with Calypso on her island. She serves as a signficant temptation to Odysseus, not only offering him physical pleasure, but also offering to make him immortal. In Odyssey 5, Calypso tells Hermes that she "promised to make him immortal and un-aging" (A.S. Kline translation).
Despite this temptation, "the Nymph no longer pleased" Odysseus, who missed his native land and his family. Furthermore, Calypso was compelling Odysseus to be her sexual partner: "He was forced to sleep with her in the hollow cave at night, as she wished though he did not".
Thus, given the amount of time Odysseus spends with Calypso and the temptation she offers, I think I would rank her among the top three along with Athene and Poseidon.