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(Eurymachos:) ‘[…] in any case we fear no one, and surely not Telemachos, for all he is so eloquent. Nor do we care for any prophecy, which you, old sir, may tell us, which will not happen, and will make you even more hated.’
Eurymachos and the suitors disrespect the gods by dismissing Telemachos, who is favored by Athene, and Halitherses, who speaks the gods’ will. By laughing off the words of those through whom the gods speak, they are placing themselves in opposition to divine law. So they will be punished.
When they had made fast the running gear all along the black ship, then they set up the mixing bowls, filling them brimful with wine, and poured to the gods immortal and everlasting but beyond all other gods they poured to Zeus’ gray-eyed daughter. (2.430-433)
Pouring out perfectly good wine (and burning perfectly good ram's thighs) definitely sounds like a "sacrifice": it's a good way to convince the gods that you take them seriously.
They came to Pylos, Neleus’ strong-founded citadel, where the people on the shore of the sea were making sacrifice of bulls who were all black to the dark-haired Earthshaker. There were nine settlements of them, and in each five hundred holdings, and from each of these nine bulls were provided. (3.4-8)
The residents show their piety by holding ritual sacrifices to their patron god, Poseidon. Their piety implicitly renders Nestor, ruler of this land, a trustworthy friend for Telemachos.