There is internal and external evidence that the Bible comes from other sources. Whether the repetitions (Moses and the rock) or known other versions (Noah story). Do we have anything similar for either of Homer's epics. I know we have evidence that something Troy like existed and there were probably some sort of wars. But I was thinking even more about all those Odysseus stories, the Sirens and Cyclops and Circe and the pigs. These seems like they could have been independent stories that were pulled together.
There is strong evidence that parts of Homer's works are much older than their attributed date, and that components are part of a larger Indo-European epic tradition.
One great starting point is a Bryn Mawr symposium volume, Troy and the Trojan War. It's available in its entirety online: http://repository.brynmawr.edu/cgi/viewcontent.cgi?article=1006&context=bmc_books
If you have any linguistic background, the very best (in my opinion) on the subject of the Indo-European tradition is Cal Watkins' How to Kill a Dragon: Aspects of Indo-European Poetics.
On evidence for earlier sources, there are a few lines in Homer that don't scan properly as dactylic hexameter lines. However, if the Greek is changed to a pre-Mycenaean form of the dialect (ca 1500BC, if I recall correctly), all of those lines scan perfectly. This is generally accepted as evidence of much earlier folk tales being incorporated into the narrative. On the subject:
Ruijgh C. J. "D’ Homère aux origines proto-mycéniennes dela tradition épique: analyse dialectologique du langage homérique, avec un excursus sur la création de l’alphabet grec" // J. P. Crielaard (ed.) Homeric Questions: Essays in Philology, Ancient History and Archaeology Amsterdam. P. 1–92.