Well, to be blunt, I'm not sure they do. A spell is cast over Odysseus as early as Book 2, and the gods are present in Book 1. Odysseus then moves into a series of adventures, many of which definitely involve magic. However, he vanquishes the suitors through his own prowess—and his final exchanges with Penelope that prove his identity are magic-free. It's more like the book starts in a mundane world, moves through a time of much magic, then returns to the mundane (if violent)—plus a trip to Hades to wrap things up.