Greek myth doesn't work like that. It's a collection of stories from different authors, times, and places passed on through a mostly oral tradition. Sometimes people got interested in these things and gathered collections of stories - almost always very boring, since they are stripped of literary quality.

Probably the best known encyclopedia of Greek myth is Appolodorus' Library, which does exist in English translation (I think this is the edition we used). I had to teach this as a TA one term. It is hell.

Greek myth is older than our sources for it, and Hercules is a nice example of this. The Iliad and Odyssey existed in a wider corpus of oral epic, almost all of which has been lost except for summaries. The Iliad and Odyssey occasionally make nods towards these other epics in a way that assumes the audience would be familiar with them. Some people (I'm thinking of Nagy mainly) have tried to do reading of the Iliad and Odyssey informed by these as best they can.

Hercules is one of these strange references. He is present by implication in the Iliad, even if his name doesn't come up anywhere (I can't remember if it does), and in the Odyssey he's one of the characters Odysseus sees in the underworld. Homer makes an odd comment about that; Odysseus sees the shade of Hercules only; Hercules himself lives on Olympus. That suggests to me that apotheosis isn't fully developed in Homer, but I don't think I've seen any articles on it.

Specific stories about Hercules get told in different places; there are aitia that pop up in various works giving Hercules as the founder of a number of cities, shrines, or cults, he appears as a character, either central or peripheral, in a number of plays, he has a small role in the Argonautica.

The earliest thing that I can think of that might be considered a canonical treatment might be the metopes of the temple of Zeus at Olympus, that illustrate his 12 labors. I'm sure archeologists around here have more to say about those than I will ever know.

Keep in mind when consulting any translated source that the act of translation is inherently imperfect, especially so in the case of sources from long ago. A translation is never an exact analogue of the original work, as each translator makes decisions differently and prioritizes things differently when translating any text. There is no such thing as a "completely untouched" translation because the act of translating a source can lead to the loss or change of emphasis, meaning, or other aspects of a work.

Related question, do we know the origins of Herakles? We know him most prominently from the Greek Pantheon, but I've read that his legend and his cult was established as far as in Asia Minor, North Africa, and parts of Europe.

I have a copy of Classical Gods and Heroes: Myths as told by the ancient authors and it seems pretty good. It is translated into English, however the translations are of specific sources rather than an author recreating the narrative herself.