(おがむ) Literally, to pray (at a Shinto temple). Figuratively, to worship the ground someone walks on. 拝む also means “to contemplate”, like a stalker his idol of choice, his face like he’s looking at God himself
(いのる) Literally, to pray (Christian style). Figuratively, to wish (for good weather, long life to your friends, to pass this fuckin’ math test). Emphasizes the ACT of prayer, rather than the contents.
(きがん) A figurative prayer or wish, made to pass a test or to not go to jail, etc.