In my active days, we had guys who were 7-year-actives who only withdrew from the university after their grades caught up with them. We also had guys who are now department chairs at major universities. So today -- we would likely be called a balanced chapter. I know it's hard for some guys to realize that their fraternity days are over. Your problem alumni will sooner or later come to that realization.
They are alumni now - they should only be participating in alumni activities. If they want to be actives again, they need to re-enroll in your university.
About the house. Get your housing corporation involved. There are some inexpensive security things you can do. Some in the $60 range. But what you can do depends on the laws in your state. So I'm not going to make any suggestions. You should have a house manager who is in contact with your housing corporation. It is important that you chapter and your housing corporation get a handle on what's going on at your house. I know of a university that will suspend a chapter for the conduct of alumni while they are visiting your chapter house, even if no actives are involved in the conduct.
Tell the guys crashing your party that the sororities are conditioning their participation on the fact that only current actives would be attending.
Greek Chat is not going to solve all of your problems here, but many of the folks commenting have a lot of experience and your problems are not really new or unique - but they are solvable.
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