How does food in the Odyssey tell us something about Greek culture?
In contrast to the Iliad, Homer's Odyssey has a more domestic feel to it. One manifestation of this is the fact that the characters in the Odyssey are constantly feasting. The main staples of the Homeric diet are wine mixed with water, bread, cheese, and roasted meat (from sheep or goats).
Whereas wine and cheese would have been common part of the Greek diet, I doubt that the ancient Greeks ate as much meat as Homeric poetry portrays them as doing. I'm surprised that Homer does not mention the consumption of fish more frequently. In fact, in Odyssey 12, Odysseus' crew seem unsatisfied wiht fishing and they kill the forbidden cattle of the Sun for food.
In my opinion, the most interesting thing we learn about Greek culture in the Homeric epics is not what they eat but the way they behave in dining contexts. Polite Greeks, even the poorest (like the swineherd Eumaeus in Odyssey 13-16), offer strangers to their homes food and drink before even asking the stranger their name or reason for stopping by the house. In contrast, barbarians like the Cyclops feast on their guests rather than feasting them. Also, it is interesting to note that the Cyclops get drunk on the wine Odysseus gives him (a sign of his barbarity).
So, in Greek culture, it was very important to be a good host. Failure to do so could incur the wrath of the gods, especially Zeus, who was the god most associated with hospitality (Greek: xenia). Guests, though, did have some responsibility. We should note that impolite guests, like Penelope's suitors, overstay their welcome and wipe out the resources of Odysseus' home.