Piety in the Odyssey is shown by deference to the gods, submission to their will, and through gestures such as sacrifices, festivals, banquets, and prayers. It also entails respect for the dead – proper burials and rites. Impiety or direct challenges to the gods often result in suffering or death for the offender.
Although the men in the Odyssey revere the gods, that respect is not returned; the gods have little value for human life and often use men as their playthings.
In speaking of Odysseus, the people of Ithaka refer to him in language usually reserved for gods; they equate him with godliness, as does Homer, which is why those who disrespect him suffer the same consequences as those who are impious.