How does poliwhirl/wrath eat? The pokedex makes such a song and dance about his intestines, but he lost his mouth when he evolved.

Well, personally I assume they do have mouths (at the centre of the spiral, since that’s where their Water Guns originate in the anime) but that they’ve become smaller and less obvious, so we can’t actually see them in the art and sprites.  Alternatively, they may adapt to absorb nutrients directly from the water around them, although this seems unlikely to me, since Poliwhirl is supposed to be more suited to life on land than Poliwag.