As long as the house is owned by the chapter or their headquarters, it not possible for Alfred to kick the students out, because they (the school) have no ties to it. IF they do own the property then they can do whatever they want.
I don't believe that Alfred can ban you from wearing Greek letters either. That would be a violation of the first amendment it would seem.
Here's what seems to be the deal to me. For now Alfred has put a stop to the Greek System. To me this implies that they do not have a "Recognized" system anymore. So under student life and orgs., they wont be listed. This doesnt necessarily mean that Greek orgs cant exist off campus, as long as they arent on school property. If you're a local than you can keep it up pretty easily and you wouldnt have to be considered "illegal". If your org is national you could face a problem, because it would seem that since the school doesnt "recognize" the system anymore, it would seem that most nationals would consider their chapters there as inactive and you would probaly either have to go alum or go local and add or drop a letter to your name. I could be wrong about all of this however.
If Alfred U Greeks truely feel like you're in the wrong then fight it all the way
Just a thought though...In case things dont work out (I forget how far Alfred U is away from Alfred State havent been up there in awhile), but what about affiliating with the Greek orgs. at Alfred State, if they have the same orgs.? Would that be a possibility? Or even another close school? It might not be what people want, but its something.

I know that Havard doesnt have a recognized Greek system, but they have greek orgs. Does anyone know if they are locals or if they have some national letters and are they officially listed by the nationals?