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.