Vanaduke does not belong to any monster family. Thus, he does not suffer extra damage against a weapon with a vs. family bonus, although overall damage bonuses to specific weapon types will still function as normal.
However, he is weak to piercing and resistant to shadow, much like a fiend. (In his final stage, he actually becomes completely immune to shadow damage. Not that I have any idea why you'd want to bring a pure shadow damage weapon down there anyway, but still, if you really wanted to go hardcore, you could try to run FSC with nothing but an Acheron for kicks.)

Appearance and history-wise, you could make a decent argument for Vanaduke being pretty much any family other than Slime and Construct. He looks like an oversized Beast, and Gremlins are humanoid furry creatures which sort of resemble him. His lore states that he is an Undead king, and that he has been corrupted by some form of fire-based dark energy (possibly Vog, which might explain his more animalistic appearance). All this is on top of his Fiend-esque damage weaknesses and resistances.

Also, I note the spelling of 'awkward' is now correct. :B