The principal evidence of orality in the Homeric epics lies in the extensive repetition they contain. Characters are given an epithet, "swift-footed Achilles" or "many-witted Odysseus," and this is repeated every time they are mentioned. Sometimes the epithet is extended into a larger phrase. Agamemnon, for instance, is regularly addressed as "Most glorious son of Atreus, Agamemnon, lord of men." This is a phrase that takes up a whole line of heroic hexameter and is easy for the poet to memorize and regularly repeat.
Much more than this, however, there are long passages which are almost entirely repeated. In the Iliad, Agamemnon tells Odysseus, Ajax, and Phoenix the gifts he will bestow on Achilles to recompense him for the loss of Briseis. It is a long list including tripods, talents of gold, horses, women, the hand of one of his daughter's in marriage and seven cities. In book 9, the three men go to meet Achilles, and Odysseus repeats Agamemnon's list word for word. Milman Parry showed that this formulaic repetitive style is a feature of oral composition and an aid to the memory of the poet who learns and recites the epic.
We also have internal evidence of the way in which oral poetry was recited from memory in the description of the blind bard Demodocus in the Odyssey, playing the lyre and singing a story of Odysseus to the man himself at the court of King Alcinous.