Question: What does the Odyssey say about ancient Greek values?
Answer: Athena embodies what the Greeks viewed as most important--cunning. Odysseus was the closest a human could get to the wisdom of Athena. Throw in his bravery and fighting prowess, and despite his flaws, we have the greatest of Greek heroes. The Odyssey also shows the honor of being a faithful wife. Penelope remains loyal to her husband even though Odysseus has not remained loyal to her. The Greeks also placed much importance on hospitality, showing what happens to those who break this sacred host/guest bond when the suitors are slaughtered.
Question: What are some examples of Odysseus' cunning and wisdom?
Answer: He thinks of the Wooden Horse stratagem. He fools Polyphemus with the name "Nohbdy." He ties himself to the ship's prow so he could hear the Sirens without being tempted to seek them. He comes in disguise to the suitors.
Question: What role do the gods play in The Odyssey?
Answer: In classical mythology, the gods are nothing more than immortal humans with super powers. It's this combination--super powers, immortality, and human weakness--that causes so much trouble. For example, Athena takes pride in Odysseus; Calypso, a minor goddess, lusts after Odysseus; Helios wants revenge on Odysseus' crew; The Trojan war began on account of jealous goddesses.
A film adaptation of The Odyssey contains a scene with a struggling Odysseus caught in a storm after leaving Calypso's Island. On the brink of death, Odysseus yells, "What do you want me to learn?" Poseidon responds, "That without the gods, man is nothing." Although this scene does not occur in the actual epic, it summarizes the necessity of having respect for the gods in The Odyssey.