Roles of women in the Odyssey reflect the actual customs of archaic Greece, although certain characters who only appear in the backstory, such as the powerful queen, Clytemnestra, may have reflected older Mycenean traditions.
The main role in which we see women in Homeric epic is domestic, as part of the "oikos" or household, and responsible primarily for weaving cloth and food preparation. Penelope's weaving is not only a plot device, but reflects the central economic function of women in large households of producing clothing. Women are generally portrayed as wives, potential wives, or as objects of sexual desire.
Female divinities or semi-divinities play an important part in the plot of the Odyssey, with Athena protecting Odysseus and Telemachus, and the sirens, Circe, and Calypso, inter alia, acting as potential obstacles to the return.
You can find an excellent portrayal of women in The Odyssey in Margaret Atwood's The Penelopiad. That said, notice that the very few women in the story make only brief appearances. Even Penelope, by far the most important one, is mostly spoken of. Anyway, each woman stands for a different archetype. Penelope is the faithful wife whose guile protects her husband's estate from the suitor's greed. She's also a mother contending with the ineluctable fact that her teenage son will no longer be ruled by her, and a kind mistress to a bunch of -with some exceptions- treacherous servants who more or less openly serve what they deem will, in the long run, be the winning side; namely, the suitors. Bold and determined when alone, once her husband is back and her prudent test of his identity is satisfied, Penelope contentedly stands in his shadow as he regains his authority.
Old Euryclea seconds Penelope, watches over the maids, and keeps her eyes and ears open to the schemes devised by the suitors. As Ulysses' former nurse, she's instrumental in ascertaining that he's no fraud when, on his return, she bathes him and recognizes an old scar on his leg. At times one has the feeling that the whole Laertian household would collapse were it not for her moral strength and unyielding belief in the return of the master.
Helen, true to her nature, plays the gracious hostess to Telemachus when his quest takes him to Sparta. Nothing in her demeanor hints to her shady past; it's as if she has never cuckolded her husband, let alone kindled a war that cost so many lives. (We know the war was due to other reasons, but need to stick to Homer's version.) Menelaus dotes on her as on day one; these two have succeeded in erasing the past, which has taken on the characteristics of a narration.
Nausicaa is a clever literary device to introduce Ulysses into the Phaeacian royal palace, where her mother, Queen Arete, encourages her husband to aid the hero. While Arete clearly stands for the dominant wife, she doesn't flaunt her power for, as every woman knows, in a world of men, sweetness achieves better results than authoritarianism. Although Nausicaa was engaged to some prince, the Phaeacian monarchs offer her in marriage to Ulysses, an offer that he of course refuses but that stresses her role as a compassionate soul (see the scene on the beach) and an obedient daughter.
Penelope's maids do not differ much from one another, but Melantho is the one whose voice and behavior stand out. The maids' attachment to the suitors could be understood as a desire to cast off their anonymity, or as a manner of survival if they were threatened with rape and ill-use. The part they played in the story and their execution at the end is open to debate, which brings us back to Atwood's novel. She provides a wonderful explanation of the murders, one that is too intricate to summarize in this brief comment.