Greeks were all illiterate at the time of the Homeric composition. They didn’t start reading/writing again for about fifty years. Arguably, these stories made the Greeks reintroduce writing.
There is the argument on who’s that Homer anyway, and my conclusion (after studying the Epic cycle for some years) is that the Iliad was the composition of ~800 years of oral tradition. The Odyssey was produced in a short time afterwards. Homer had a school of acolytes who composed The Odyssey together. No one who has read The Odyssey more than three times will say with confidence that the whole composition is produced by one person. The narratives among the books are too different. It was a tomb for relating to the way Grecians once were … before the Dorian invasion which hobbled them all back into illiteracy, and how they should live once more. Soon after these works came the “golden area” of philosophers.
Oh yeah, the actual Trojan war occurred ~800 years before Homer composed the Iliad! Soon after this epic blood letting the Dorians (some illiterate inland tribal peoples) walked right over them, causing the gap between ancient and classical Greece. Perilous time for Humanity.
The Epic cycle was actually a dozen or so comparable stories, only Homer’s survived in full. Interesting side stories include that of Iphigenia, which explains Clytemnestra’s betrayal more than the woman hating rhetoric spewed by Agamemnon (in hades) or other accounts.