My brother has had strokes and he and my mother are owners of a home, they live in with a non working sister and another brother.
Can my brother that name is on the deed of the house,that has had strokes evicted my non working sister.

The owners of the house can evict any non-owner living in the house. But all owners have to agree.

And, to my knowledge the fact that he has had strokes or his sister doesn't work has very little to do with it.