I consider 'normal' to be a lack of specialized training. Basically, anything that muddles through life without special elemental powers is 'normal' to me. These things get stab to normal moves because they resort to them more often to survive.
Thus, Jigglypuff and Snorlax get stab to body slam, but Hitmonlee does not, because it's awkward for him to abandon his training and resort to a move like that as an attack.
Birds rely partly on their anatomy, and partly on their powers of flight, thus normal and flying. Pure flying types should be deities and clouds and stuff, and there SHOULD be some birds who are flying type pure, like a hummingbird who would rarely use its body's physical prowess to survive and instead, relies primarily on the power of flight.
Not a perfect approximation, perhaps, but it makes sense in my head.
Oh, and the weakness to Hero and ignorance of ghost is because their lack of connection to elemental powers lets them lead a simpler existence than most of their elemental pokebretheren.
I know, autism, but that's how it works in my head, fuck off.