I am wondering if there is a knightly order similar to the Grey Knights of 40k. I am thinking, perhaps, a highly militant group of knights who often adventure with witch hunters, and whose primary oath/duty is to hunt down demons/demonic influence and destroy it. Is there anything like that in the Old World?

http://warhammeronline.wikia.com/wiki/Renowned_Empire_Knightly_Orders

Maybe the Hunters of Sigmar or the Order of the Hammers of Sigmar might be somewhat akin to what you're looking.

However, what you're describing for Warhammer amounts pretty much to a Witch Hunter, imho. Just a noble one.

How about the Knights of the White Wolf? It is said that their motto is "never suffer a mutant to live", and that they frequently venture into the Drak Wald to hunt mutants and beastmen (see Middenheim: City of Chaos).