I'm in a tight spot right now, I've been living with a family member here in New Jersey for a little over a year. There was never any lease signed, I've just been living in a room in her house. Things have gotten bad between us, and on Fri, she informed me that she wants me and my belongings out by Sun. Even though I have nothing in writing, I feel that I should at least have some time to get my things together and make plans. And if I were to leave, but left my possessions to be gotten at another time, aren't they protected in some way?
Also, sorry about the heading. Obviously I meant to say eviction without lease.

Depends on your state or country. In most of the US a living arrangement without a lease requires that you are given at least the amount of time between your payments to get out of a place. Like if you pay monthly you have to be given a month to get out. She shouldn't be able to lock you out as long as your stuff is still there, she should have to follow proper eviction procedures. I would try to talk with her, I understand it is bad between you so maybe you could get a third party to mediate the conflict between you two. Since you probably want to leave, it's just a matter of how much time she gives you to do that. Come to an agreement and get it in writing.