Spinach is healthy. Popeye eats a lot of spinach; it's his favorite food. So he is incredibly healthy and strong, especially right after he eats some.
It's as simple as that. Popeye explains in his song:
I'm strong to the fin-ich,
'Cause I eats me spinch.
As to whether he's an alien or mutant or something:
I yam what I yam, and that's all I yam.
