The Homeric epic as we have come to understand it is actually a kind of collective oral poetry, memorised, rendered and promulgated through a series of techniques, most notably formulae. One such formula is a "common epithet" associated with characters, somewhat famously, "cow-eyed" Hera, for Zeus’ wife. Another is, for example, a catalogue, an eldless barrage of names, locations, places, etc. common across many epic oral traditions.
The singer/performer (in Homer’s time there were special bards specifically of Homer’s texts called rhapsodes) would use these formulae to help them construct the flow and meter of the overall poem while rendering. So they basically knew the formulae by heart, knew the general plot outline, and had enough cultural and other vocabulary to be able to reconstruct a long text in a single sitting from memory.
This means that most of the time, every performance was unique, and small details were continually added and altered by every rhapsode / performer. Hence, while the outline remained fairly known, the details have naturally shifted over the years. Hence the mountains of inconsistencies with for instance armour, customs, etc. Even though the story is set in the Bronze age, most dress and probably some of the cultural aspects in general is a mix of stuff contemporary to the time of writing and stuff the Greeks may have thought seemed old to them.
It was, by and large, more important to remember the overall details about what the key characters do than it was to remember what they wore for centuries on. For the purposes of plot, armour is armour after all. (Incidentally, this is why the description of Achiles’ shield in the Illiad is such an interesting example.)
Given all of this, today it’s generally accepted that "Homer" was not a singular poet of tremendous gifts who bequeathed the world two immense poems, but rather a name for a collective author. This hypothesis was borne out by Milman Parry and Albert B. Lord in their research in Yugoslavian oral poetry in the early XX century, where they found living examples of singers able to, in several sittings, render some 12k+ verses from memory.
This is by no means unique, and similarities have since been found across cultures, though, perhaps, not to that extent. Blues is, for example, full of constant epithets and other formulae that make constructing and reconstructing songs or indeed improvising them in a call-and-response manner much easier. As long as you have the cultural cachet and knowledge of the building blocks, that is.