Omen birds are an important theme in the Odyssey. They are important prophecies. Omen birds play a much stronger part in Ithaca and in Telemachus's story than in the Odyssey. In The Odyssey, omen birds foretell the killing of the suitors, Odysseus's homecoming, and reassure Telemachus that his house will remain powerful.
In The Odyssey, when the Telemachy is starting and Telemachus first addresses the suitors, and says "If you think it a sounder scheme to destroy one man's estate and not make restitution, then eat your fill, while I pray that Zeus will bring a say of reckoning, when in this house I will destroy you, and not make restitution."(Book 2, lines 140-144) to warn them that if they do not leave his house, eventually they will be killed, as he speaks, Zeus sends two eagles to fly over the suitors. This prophecy foretells the massacre of the suitors, but none listen.
In book fifteen, Telemachus Returns, when he is with Menelaus, about to leave and return to Ithaca, an eagle flies from the right carrying a goose from the yard. Helen says "Just as this eagle came down from his native mountains and pounced on our home-fed goose, so shall Odysseus, after many hardships and many wanderings, reach his home and have his revenge. Or he is already there and planning trouble for the whole pack of Suitors!" (Book 15, lines 172-179). This omen compares Odysseus to the eagle, and the suitors to the goose, which is helpless against the eagle.
When Telemachus finally lands on the shore of Ithaca, he doubts that they will be able to stop his wife from marrying a suitor. He is talking to Theoclymenus when Apollo's bird, the hawk, flies by holding a dove. Theoclymenus pulls Telemachus away and says...