Calypso keeps Odysseus on Ogygia for a long time. During this period Odysseus sleeps with Calypso- “they found pleasure in making love”- and this time not by Hermes’s orders. This suggests at least physical appreciation of the goddess’s company, although Homer does also say that Odysseus “had to sleep with her”. The line “The Nymph had long since ceased to please” gives the impression that sometime in the past Odysseus perhaps enjoyed her company. From what Homer tells us, not once in the seven years or so does Odysseus try to escape, which could indicate feelings for the Nymph, but could also merely be due to a lack of an escape route and a wish not to drown on the seas. Although we have no indication of his wish to escape, we have plenty of references to Odysseus’s pining for home, and these indicate his nostos, or homesickness, and show that Calypso not only holds him prisoner on the island, but shows his lack of feelings for the goddess. For instance, when Hermes first arrives in Ogygia, Odysseus is not in the cave with Calypso, but on the shore, “tormenting himself with tears and sighs”. When Calypso finds him there later, his “eyes were wet with weeping as they always were”, and when she offers him help to leave, he announces that going home is his “never-failing wish”. Calypso offers him immortality, but his love for his wife is too strong, and this implies that he cannot have feelings for another. This is echoed by the line “never for a moment did she [Calypso] win my heart”, which is what Odysseus says to Alcinous about his time with Calypso. When he does eventually leave the island, it is “with a happy heart”, and this too shows his wish to leave Calypso and her island far behind. All in all, Odysseus describes the way he ends up on the island as a “misfortune”, and that sums up his feelings for Calypso quite well.
The next woman Odysseus meets is mortal, though distantly descended from Poseidon. Nausicaa is the first normal woman Odysseus sees in nearly 20years, the last of whom being the women from Ismarus, the city he sacks directly after leaving Troy, and understandably he is very weary of her. Despite this, or perhaps because of it, he treats her with the utmost respect and keeps his distance from her, both physically and emotionally. He admires her beauty, and says that she looks like Artemis- “it is of Artemis…that your beauty grace and stature most remind me”. He respects her decisions, and listens to her like an equal, despite her age and sex, which shows respect, although not necessarily feelings. He also wishes on her a husband – “may they give you a husband and a home” and a blessed life- “may the gods grant you your heart’s desire”, which shows his veneration for her. However, though he wishes this, at no point does he indicate that he would be her husband, and this suggests that his feelings for her are not romantic. After Odysseus leaves Nausicaa in the town, Homer does not mention her anymore but for their goodbyes, despite the fact they are staying under the same roof. This indicates Odysseus’s lack of interest in Nausicaa’s comings and goings.
When Odysseus meets Nausicaa’s mother, he clasps her knees. This could be interpreted as a display of affection, but is more likely to be Odysseus following his advice from both the disguised Athene and Nausicaa. Odysseus also shows respect for Arete by answering her questions, as normally he would expect to hear them from the master of the house. Here again though, merely answering questions does not prove affection for Arete, as it is polite to answer questions, and he is in her house and asking for her help.
Overall I consider that Odysseus does not care about these women. He loves his wife dearly- “[Penelope] is never out of your thoughts”- and is happy to leave every island he sets foot upon if he thinks he is heading for home. Circe does seem to hold a certain place in Odysseus’ heart, because she is the one he stays with voluntarily and has to be persuaded to leave, but Odysseus leaves the others without a backward glance- “with a happy heart” in fact, in the case of Calypso. Odysseus’s affection and respect for Nausicaa seems to be purely polite and possibly only to suit his own means, or at the most brotherly- he wants the best for her. As for Arete, Odysseus never had affectionate feelings for her. He needs her support to get home, and this is the only reason he shows respect for her, except perhaps because she is a wise woman. Throughout the Odyssey, Odysseus longs for his homeland, and is unable to feel much but grief at his prolonged absence.