People frequently reference the stories' events as part of Greek mythology but they are usually thought of as works of fiction, not prophecy. So if they were then what was the precedent for stories, sch as the above or plays, becoming religious canon. If they weren't then what was the basis ancient Greek faith, their Bible so to speak?
No. The Homeric poems only really became popularised in the late 6th century BCE, 100-150 years after they were composed. After that point they did hold a great deal of cultural authority, in a comparable way to Shakespeare or Pushkin: the Greeks regarded them as iconic of their shared culture, and would quote from them regularly, and yes, sometimes even cite them as sources for details about the gods. No other texts held anything like the same level of cultural hegemony.
That doesn't make them a bible, though. People could just as easily cite them to contradict them. The context is often something like "I agree with Homer, who makes Zeus stronger than all the other gods put together, when he says in Iliad 8..." In other words Homer gets cited as a classic example, not as an authority.
There was no bible, and indeed there's no particular obligation for any religion to have one. There was no centrally organised Greek religion, and even the pan-Hellenic aspects of Greek religion were associated with specific cult-sites: Delos and Delphi for Apollo, Olympia, Crete, and Dodona for Zeus, Argos for Hera, Athens for Athena, Epidauros for Asklepios, and so on. These separate cults could to some extent be conflated to create a common heritage, as was done in the Hesiodic Theogony, but that was always really an artificial superimposition on top of the local religious centres and practices that dominated the ancient Greeks' religious life.
There were also truly shared forms of religious experience that were non-local in character, but we tend to distinguish these as something different, and call them "mystery" religions. This is where we tend to find religious texts that are more comparable to a "bible", though even there the comparison is a stretch. These texts contained a certain amount of religious dogma, but only one text survives intact, the Hymn to Demeter, and to a novice even that looks more like a conventional mythological text than something particularly religious. Elements from these dogmatic traditions do crop up in other more mainstream literature though, even in Homer (esp. in Iliad 14, where a few passages contain references to Orphic theogonic traditions), but only as allusions.
In The Republic Plato complains about The Odyssey because it portrays the Greek gods as petty beings. Thought I should add that to /u/rosemary85 's post.