Homer's stories, most Greek plays. One could argue those fit the bill.

Off the top of my head, all those were orally preserved and now we can (and should) read them. I'm sure someone else will give a more in depth answer.

This is some recent work on relating aboriginal oral histories in Australia to major climatic and geologic shifts in the deep past (more than 6,000 years ago).

The hymns of the Rig Veda. But those aren't stories...