It's a complicated question, in part because it requires an interdisciplinary approach, combining history, social science, psychology, anthropology, ethnography, linguistics, and other fields of study.

The two major figures on this question I think are Marshall Macluhan and Walter Ong, particularly the latter's Orality and Literacy.

Its been a while since I read Ong, but I can recall objecting to a number of his ideas in the context of Arabic and Arabic history.

In reference to your question, it's not merely the question of a transition from illiteracy to literacy but also what writing does and what kind of writing you're doing. Part of the work of someone like MacLuhan was demonstrating how the technology of different kinds of writing, particularly the advent of print, changes how we interact with that writing.

In my own area of study, which was culturally resistant to print culture despite having a literate culture, that had some really interesting ramifications. Brinkley Messick's The Calligraphic State: Textual Domination and History in a Muslim Society gives some really interesting examples.

Many of his examples relate to what these texts were and what they did. Sacred or authoritative texts, in particular, bore a different relationship, particularly when they were originally intended to be memorized and recited aloud and the written text was intended perhaps at most as an aide memoir. The Quran is the example ne plus ultra of this.

I haven't read it and it's outside my area of knowledge, but in a European context I believe Paul Saenger's Space Between Words: The Origins of Silent Reading is supposed to be excellent.

To add a bit of context here: the field of folklore demonstrates that everyone has folklore and that there is an element of oral culture in all societies - literate or not. That doesn't affect the legitimate nature of your question, but it is important to remember that becoming literate - as a person or a society - does not turn off the 'oral switch'.