There are many thousands of books and articles on ancient Greek religion. As you classified this under Homer's Odyssey, the most relevant works would probably be ones that talk about the Homeric epics or early Greek religion.
An excellent starting point for research on classical topics in general is the website of the Society for Classical Studies. Your university library website should provide access to L'Année philologique, a searchable database of articles on classic studies that is the standard research tool in the discipline.
Another good starting point for your research would be Walter Burkert's Greek Religion, which covers in great detail the idea that rather than ritual enacting myth, the stories of the Greek gods may have instead originated in an attempt to explain religious ritual.
Paul Veyne's book, Did the Greeks Believe in Their Myths?, is a good starting point for thinking about how the original audience would have understood Homer. Veyne argues convincingly that the ancient audience would not have believed Homeric epics and their stories about the gods literally.
As the Homeric epics are part of an oral tradition, another good starting point would be books on Homer as oral tradition literature such as Walter Ong's Orality and Literacy or Eric Havelock's The Muse Learns to Write.