I don't think he's human. I one account he says about how he would attend meetings of the black eagle and the people would freeze for a moment with fear. They recognized him as the man who had been there with their fathers fathers to create the order. He says how he watched the sons take the fathers place, "AGED NOT BY TIME, but by anguish."
It is hinted at in several notes and memory tubes that he is from another dimension and he was banished for some reason. DamnNohtml's CS "Through the Portal" does a very good job trying to explain Amnesia's backstory.
EDIT:
Spoiler below!
Quote:The Immortal Baron
The Baron of Brennenburg lives a reclusive life with his family at his castle nearby Altstadt and like most those of noble birth, rumors are inherited alongside with the title. Researching the history reveals little before the castle was consumed by fire in the late 16th century. It was rebuilt by Alexander, a nobleman from the Rhinelands claiming the role as protector of the Prussian State. Alexander helped the region to flourish and remained popular throughout his presumed lifetime. The family has always been secretive when it comes to lineage and heritage, therefore the birth and death of Alexander and his offspring has never been fully recorded. This has fed the idea that the baron is in fact the one and the same who came from the West over three hundred years ago, lived through the time of occupation, and joined the coveted Order of the Black Eagle along with the great leaders of this country.
Quote:One day I will return. If it wasn't for the thought of you, my love, I wouldn't be able to go on. When I find myself doing terrible things, I take comfort in you.
As long as I am able to think of you and long for a life together, I know I'm better than the others. I weep for them, they lust for power without restraint, where I only crave fair judgment and a safe return.
Quote:The Black Eagle fears me and after Napoleon's defeat it is only a matter of time before they will demand my head on a platter. I must remove myself from this land. This time it must work. If I can't return home now, I shall perish.
Quote:They all know I am the one and same Alexander who helped their fathers and grandfathers to found this great Order. I've seen them take their fathers' places, and they too will grow old and pass away. While I remain the same, aged not by time, but by anguish.
I think he's a human that committed rituals of some kind to extend his life tremendously. Also, he might have at one time been a traveler of worlds, but was left behind.
Or, you know, what Corinthian said.
He has definitely taken on the shape of a human, cause no one questioned him being one while he acted the Baron. Same thing with Agrippa; they look human but I don't think they are.