"Oral poetry" refers to those forms of poetry which are composed during delivery; instead of being written and memorized, they are put together from memorized component-parts during the performance, according to the requirements of meter and the circumstances of the situation. The story-line may be well known to the audience.
The hip-hop version of oral poetry is freestyling.
That a traditional poem (such as the Odyssee) was orally composed is revealed by the many "formulaic" (i.e., pre-fab) parts; formulaic parts have known metric features and can easily be fitted into a line.

Quotes from R.Finnegan, Oral Poetry:

'The need for the "next" line is upon [the poet] even before he utters the final syllable of a line' (Lord 1968: 54). So the singer builds patterns of sequences of lines added to each other in a series of parallel sentences." (63)
'Homeric epithets' are often combined with other formulaic phrases‹repeated word groups‹which have the right metrical qualities to fit the first part of the line. So a whole line can be rapidly and easily constructed by the oral poet, built from a ready-made diction. On other occasions, other combinations are possible from similar metrical units, to give the necessary sense. Thus, 'in composing, [the poet] will do no more than put together for his needs phrases which he has often heard or used himself, and which, grouping themselves in accordance with a fixed pattern of thought, come naturally to make the sentence and the verse' (Parry 1930: 77; Finnegan, p.59)
This formulaic style [proves] ... that the Homeric poems were orally composed. It was the need of the oral poet ... for fluent and uninterrupted delivery throughout a lengthy performance that made the formulaic style both necessary and suitable. The peot had a store of ready-made diction already tailored to suit the metrical constraints of the hexameter line. By manipulating formulaic elements from this story‹the 'building blocks'‹he could construct a poem based on traditional material which was still his own unique and personal composition. The poet had at his disposal this series of traditional patterns built up over the years ...., but he was not passively dominated by them: he used them to create his own poems as he performed them. (60) Again, parallelism or rhythmic and grammatical repetition is central to this mode of composing poetry, The singer has to compose a series of lines, one after the other.