Its an interesting question. There is a likely and fairly simple answer, but to really understand that answer, I think It’ll be very useful to expand on exactly how the Odyssey/Iliad came to be written down for you! I’m going to assume that you know relatively little about the background/creation of them, just for thoroughness’ sake.

The first thing to bear in mind is that the version you have is presumably a translation from the Greek. This Greek, however, isn’t the ‘original’ Greek ( and even saying that there’s an original is opening a can of worms that I’ll get into later). There are several ways that texts can reach us in the modern day. The first is through a manuscript tradition. This means that the text has been preserved by being repeatedly copied. As you can probably imagine, relying on the copy of a copy of a copy etc. brings a whole host of problems.

The result of this copying is that mistakes are introduced. There are a number of ways that a mistake could crop up. A scribe could simply make a spelling mistake. Likewise they might misread the handwriting of the previous scribe. They might look away for a moment and then restart their copying slightly earlier than they should, meaning that they duplicate a line or section.

From these innocent mistakes, more and more problems can crop up. If you see a spelling mistake, its easy to correct, right? Well not really. It might not have been a mistake to begin with, it might just be a dialectal variation that you didn’t recognise. You might try and correct a mistake, but correct it incorrectly, effectively making that part of the text two steps removed from the original! Its quite surprising how easy it is for meaning to be changed just by a single letter or couple of letters, particularly in Greek.

As well as these basic errors, you might have interpolations. These are errors that have cropped up from outside a text. The person who last copied it might have left a note in the margin that was intended just to explain the previous line. Then the next person to come along assumes that it was an intended part of the text and simply adds it into their copy, not even placing it into the margin.

The end result of this is that every edition of an ancient text is different. Sometimes in small ways and sometimes in large. Its the job of the editor to try and restore the original text as far as possible. They try and make corrections if there’s an obvious error (for example a copy of a piece poetry might have made a mistake that means it doesn’t fit into whatever poetic metre they’re using, making it reasonably obvious that there is a probable error.) Some texts are very compromised and unstable, others less so.

If we’re fortunate some or all of the text may have come to us by another means. The other main way that this happens is through papyri, an extremely common writing material in ancient Egypt. Papyri tend to survive extremely well when either completely waterlogged or extremely dry. Naturally this means that ludicrous amounts of papyri have been dug up over the years from Egypt, many of which can shed new light on texts that have also survived as manuscripts. In general, the earlier version is considered the more reliable and papyri can easily stretch to 2000 years old and often older.

So, pushing backwards in time, what does this mean for the Iliad and Odyssey? I’ve suggested that what we have today is the end point of a long tradition of copies, but there must have been an original to be copied from, right? So who created this? This is where things get really hairy and we need to talk Analysts, Unitarians, and the Homeric question.

Debate has raged, mostly cordially, for centuries over the ‘Homeric Question.’ i.e. Who was Homer? Did he even exist to begin with?

Through the 18th,19th and early 20th centuries arguments about authorship broadly fell into the two camps of Unitarians and Analysts. At the same time, understanding of how the Odyssey/Iliad might have come about greatly expanded. Notably with the suggestion that they were transmitted orally (I.e. By speech) before being later written down.

Analysts argued that there was no unifying author to the Iliad and that it was simply a collection of different authors whose works were put together retrospectively. Plenty of this argument relies on a lot of immensely complicated linguistics. For a simple example, there are multiple dialects of Greek present, which seems like an odd thing for a single author to have done. At the other end of the scale, analysis of various word forms, contractions of vowels and the like have been used to suggest that book 24 of the Odyssey is a much later addition than much of the text.

Unitarians, on the other hand, argued that there was a singular authorial intent and vision. Some of the problems pointed out by analysts could be explained by arguing that they were later additions, mistakes of transmission etc. These arguments tended more towards literary criticism than the more concrete linguistic foundation of many analysts.

I briefly touched on earlier on the idea that these poems might have been created orally; that is that they weren’t originally written down but were created to be spoken, not read. Not only this, but also they were semi-improvisational. There would be an understanding of the overall story, but the details would be filled in as the poet went along

In the early/mid 20th century, Milman Parry and Albert Lord conducted an exhaustive study on Yugoslavian oral poetry. They recorded large volumes of poetry that was transmitted orally between largely illiterate bards. By doing so they were able to greatly support a number of theories about the potential oral tradition of ancient Greek epics.

Here’s one example of this. There’s a peculiar feature of the Odyssey and Iliad, in that they both contain large numbers of ‘stock phrases.’ You might have noticed a large number of ‘epithets’ (e.g. Dawn is often called “Rosy Fingered Dawn.”, Odysseus is often “Much Enduring” or “Great Hearted”). These very likely originate from the oral nature of their original creation. Both the Iliad and the Odyssey fit into a poetic metre called ‘dactylic hexameters,’ somewhat comparable to a modern rhyme scheme. These stock phrases all fit very easily into this metre and seem to essentially act as a pause for the oral composer. They can call these stock phrases without thinking to slot into the metre, allowing them time to think a little further ahead to how they’re going to compose the next part of the poem.

So essentially, what Parry and Lord did more or less cemented the idea that it was possible for an oral poet to create these vast poems within an oral tradition. I suspect that they eventually went a little too far down the rabbit hole when they suggested that ALL aspects of Homeric poetry were formulaic, but the basic idea is still very much sound.

Since then, scholarship has generally accepted this and moved on to looking at various other aspects of the poems, which aren’t particularly relevant to this question.

The one part of all this that is missing is exactly when, how and where these oral traditions were finally committed to writing. The unfortunate answer is that nobody can be sure. A massive range of dates have been suggested, some going ridiculously far back and others extremely late. The ‘consensus,’ if its even possible to describe it as such, is probably that they were committed to writing somewhere around the 8th century BC and are the amalgamation of a large oral tradition rather than a single author. A

So where does this all leave us, particularly in regard to your original question? It seems fair to say that the Iliad and Odyssey, as they came to us, are a result of oral tradition. These bards had a general awareness of the whole story and were capable of semi improvisationally reciting the details. How exactly these bards operated is hazy and possibly varied at different times and different places, though some suggestion of how they’re used can be perhaps be gained from the portrayal of bards in the Odyssey (see Demodocus in book 8, for example.) What is most likely is that rather than an entire performance, someone would request a specific story or a substory (say the episode of Odysseus and the Cyclops) which the bard would then give a performance of. Possibly these bards could travel from place to place, or like Demodocus in the Odyssey, they may have stayed in one place, being looked after by their host in exchange for their services.

As a play/performed story, or how much time passes in the story?