It seems to me that heroic abilities in Greek myth (Heracles' phenomenal strength and perseverance, Achilles' invulnerability, the ability of various characters to understand the speech of snakes and birds and bees, fly with cute little ankle-wings, great running speed, etc) should not require magic points or devotional pools to work; they are divine in origin, but they don't have to be activated. Also, the Greek gods are typically depicted as being able to give a divine gift, but not being able to take that gift away; to me, this says that a hero doesn't need divine approval to use his gift. If the hero does something that displeases the god, the god can put a condition on that gift (Cassandra was given the gift of prophecy by Apollo; however, when she spurned his advances, he gave her another "gift" that nobody would ever believe her prophecies.) Miracles, of course, are probably subject to divine approval, and the gods themselves manifest in some way when those are cast.
Here are some gifts that might be given to the children or favorites of the gods; it is not complete by any means. Some of them are actually from mythic heroes; others are some that seem right to me. How they translate into game terms remains to be seen.
“Godlike” strength, vigor, beauty, speed, etc.
"Impenetrable" skin, like Achilles
Acute hearing and sight
Ability to talk to/understand horses, bears, bees, dolphins, etc.
Ability to move over water, snow, unstable surfaces without hindrance
Flight (usually winged, like Calais and Zetes)
Move and/or see underwater without hindrance
Ability to dodge or parry anything, even things that cannot normally be dodged or parried
Immunity to fire, poison, other harmful substances
Regaining your “strength” when you touch the ground (like Antaeus)
Having a terrifying or awe-inspiring presence
Never fail at a particular skill
Predict weather/tell when storms are coming
Heroic Inspiration (inspiring confidence in others)
Something like the old Multimissile
Like the above, but with melee attacks, unarmed blows, etc.
Stunning Glance (paralyze with a look(
The Evil Eye (put a curse on someone)