And, on top of that, what if the folks we see in Greek mythology, like Eurydice, Orpheus, the minotaur, and Charon were also real?  How does all that work?

Well, this first season attempts to explore this with all the absolute wonderfulness that is the flawed nature of the Olympian Gods!  These people keep getting in their way, trying to avoid prophecies foretelling their demise, only to actually cause the prophecies to comes true.  Oh yeah, spoiler alert, at least one prophecy comes true, but we don't know what the repercussions are. This may be an issue to be resolved in season 2 (if there is one).

Notable absences from the pantheon include Athena, Artemis, Demeter, Hercules, and Achilles; although given the state of the Trojans in this series, Troy may already be sacked and Achilles may be dead.  

I only started watching this because of Jeff Goldbloom and Cliff Curtis, but this is a fun series and hope it gets a season 2!