[devindotcom]

It wasn't rote memorization IIRC but a highly structured retelling that used all kinds of tricks to keep it poetic (epithets for characters that took up one, two, or three syllables for instance, used without fail in those situations) but still retained flexibility. Poets would tell the story of the Iliad differently depending on the audience, and I mean they're not going to tell the whole thing every night. But there would be epic competitions where they would.

[a_bonobo]

This is correct -

there are many mnemonic devices strewn throughout the text of the Illiad and the Odyssey, for example, 'rose-fingered dawn' shows up many, many times as a 'stopping point' for remembering.

There are many, many different manuscripts of the Homer's works which all had minor or major differences, depending on who wrote them down - there's one project that tries to pull them all together: http://www.homermultitext.org/about.html

Only relatively recently has there been 'one' Iliad, before that it was whatever the orator remembered, and memory isn't perfect