is odysseus a demigod

No, technically Odysseus isn't a demigod. He was a mortal hero, a king, and one of the bravest and most resourceful heroes in Greek mythology. He is the protagonist in Homer's epic work 'The Odyssey', where we see his intelligence and cunning shine as he navigates through a multitude of challenges during his decade-long journey back to his kingdom of Ithaca. It's worth noting his mother was not a goddess, so Odysseus is, by definition, not a demigod.

Odysseus's lineage doesn’t quite fit the bill for demigod status. While Odysseus's mother is mortal, his father, Laertes, is considered to be son of Arcesius and Chalcomedusa, who are both mortals. Therefore, his bloodline is a completely human, with no direct divine lineage, which essentially distinguishes demigods from ordinary mortals. However, Odysseus's extraordinary wit and strategic mind could easily lead observers to suppose him to have a little touch of godly prowess, given the extraordinary feats he encounters in his journey chronicled in 'The Odyssey', particularly his ability to overcome challenges imposed by gods themselves. Yet, it's important to stress this does not make him a demigod in the strictest sense of Greek mythology, but rather a mortal of remarkable resilience, wit, and courage.

His capacious mind as well as his encounter with all manner of hardship indeed make him seem to us an outstanding figure: as a living human who was born into a world where gods and mythological animals prevailed, and in the end returned home not on account of any divine assistance but through perseverance and character only because he persisted in his good course.