A demon like Adversary is a fly compared to an Elder God. It makes perfect sense that a piece of Oshtur's power would allow Storm to overwhelm him. That fits with what we know from past books and Coates, who described Storm's power as a gift and heavily hinted at Oshtur in his run with the sky symbolism (walker of clouds, the blinding white light, etc.)
Asgardians were formed from the pre-conscious thoughts of mankind before humans even existed, they were formed from belief (in the loosest of terms, at least) but exist independent of prayer. They're definitely attuned to prayer and can be empowered by worship, but that isn't their sole power source. Your scans actually show that. Gods are born with innate powers they can enhance through standard magic, like Loki or Thor (who wields a mystical hammer).