Hey, Odysseus is here everybody! Yay!!!
Yes, well, be that as it may, there are still quite a few references in this part of the poem that you may not recognize, so I'll do my best to fill in the blanks.
Tithonous: Mortal husband of Eos, the dawn. In later versions of the myth, when Eos asks Zeus to grant her mortal lover immortality, she forgets to ask for him also to have eternal youth. As a result, Tithonous cannot die but continues to age until he is eventually transformed into a cicada.
Scheria: Home island of the Phaeacians. Its geographical location is unknown, though the people of the island of Corfu long claimed that their island was Scheria. Some ancient geographers maintained that Scheria was an island in the Atlantic, and some have even speculated that Scheria was in fact the same as Atlantis. (Side note: That's almost certainly completely bonkers, as Atlantis doesn't appear as a idea until 500 years later when Socrates tells its story in Plato's dialogue Timeaus.)
Phaeacians: A gentle race of brilliant ship-builders, well-loved by the gods. Their name means "gray-skinned" or "dark-skinned," so they may be a race of African as opposed to European descent.
Pieria: Region of Greece that contains Mt. Olympus.
Hermes' staff/wand: The caduceus, now used as a symbol of medicine. Two serpents entwined around a staff, often with wings at the top.
Ambrosia and nectar: The food and drink, respectively (generally--accounts vary), of the Olympian gods. While they enjoy the smell of burnt offerings, they only eat ambrosia and drink nectar. All other modern uses for the words stem from this classical origin.
Orion: A great hunter, made a constellation after his death. This, and a similar reference in The Iliad, are the earliest references to him, though later poets and writers would build on his myth.
Delos: A small island in the Aegean. Birthplace of the divine twins, Apollo and Artemis.
Demeter: Goddess of the harvest and one of the 6 brothers and sisters who were the first generation of Olympian gods along with Zeus, Poseidon, Hades, Hera, and Hestia. Her Roman name was Ceres, from which we get the word "cereal," among others. Perhaps most notable for being mother of Persephone, alongside whom she was honored in rituals that predated the era of the Olympian gods; in this way, she can be seen as one of the "Earth mother" goddesses of very early mythologies.
Iasion: A mortal man who Demeter lured away at a wedding party, where they proceeded to have sex in a furrow. After returning to the party, Zeus noticed the mud on the back of Demeter's robes, realized what the two had been doing, and promptly slew Iasion with a thunderbolt.
Styx: One of the main rivers of the underworld--often cited as the one which marks the physical boundary between the surface world and the land of the dead. The Olympian gods swore on it as their most unbreakable oath.
Pleiades: A constellation of seven stars, easily visible in the Northern Hemisphere in winter time. Often used for navigation. Originally, seven sisters, daughters of the Titan Atlas.
Bootes, the plowman: A constellation containing Arcturus, one of the brightest stars in the nighttime sky.
The Great Bear: Ursa Major, or the Big Bear--a year-round constellation in the Northern Hemisphere. It contains the sub-constellation the Big Dipper (or the Plough or the Wagon), which points North at all times.
The Hunter: Orion again. This time in constellation form.
Solymi: A mountain rage in Asia Minor.
Cadmus: An early figure in Greek myth, thought to have founded the great city of Thebes and brought the Phoenician alphabet to the Greeks. His wedding to Harmonia was the first to be blessed by gifts and the attendance of the Olympian gods, and it was during the banquet that Demeter and Iasion went off together.
Ino: A mortal who was given immortality after her death, though the reasons are unclear. This is her first appearance in Greek literature, and most of the myths about her were built up later. Generally, she was though to have raised Dionysus, the god of wine and drama, after his mother's death. Like almost all mortals who associated too closely with Dionysus, she is reported to have had a tragic ending, often involving madness and either suicide or frenzied murder. Enjoy your wine!!!