It should be noted that the Parry-Lord theory of oral-formulaic composition, developed in the 1960s and generally accepted by the 1970s due to its explanatory power and grounding in extensive fieldwork with primary oral epic (especially Slavic guslars) emphasizes that such works, including that of Homer, were not passed down by memorization but improvised in performance, from traditional building blocks of line, scene, and story.
On the line level we have the oral-formulaic epithet, which can be a noun or verb phrase that occupies approximately half a line, and perfectly fits a section of the meter of the poem, thus working as a sort of lego block for improvising in meter.
The anachronisms in oral epic were not deliberately introduced, but a result of the process of composition of traditional tales by generations of singers adding variants, and a process of what Ong calls "homeostasis", the changing of the past to reflect the present.
"Oral Tradition" refers to the manner in which stories are passed down between generations, and has been a strong force in shaping world-myths and legends. Before the advent of common writing, most stories were passed down by recitation and memorization, and The Odyssey shows many devices of oral tradition. One common device is repetition; this allowed memorization to flow easier, as many phrases and ideas remained common throughout varied stories. Another device is the use of anachronistic descriptions, meant to make the story more familiar and intimate to its audience; for example, Homer used the names of Gods and Goddesses common to his own time, instead of the original Greek names used centuries earlier. Finally, The Odyssey is written in a rhythmic style, using poetic forms to aid memorization; it is likely that earlier versions of the story were sung instead of merely recited.
One other example is the idea that the story is received from a Godly or spiritual source; in the opening lines, Homer calls on the Muse to speak through him:
Tell me, oh Muse, of that ingenious hero... Many cities did he visit, and many were the nations with whose manners and customs he was acquainted; moreover he suffered much by sea while trying to save his own life and bring his men safely home... Tell me, too, about all these things, oh daughter of Zeus, from whatsoever source you may know them.
(Homer, The Odyssey, eNotes eText)
This device allows the story to have the added appeal of seeming divinely-approved; people were more likely to repeat the stories (and pay the storyteller) if they thought they were composed by a holy hand.