What can be done if a heartless mother is throwing us out?

I live with my mother and her longtime boyfriend and have for over a year now with my two young daughters. I lost my job and was trying to get back on my feet after separating from my husband. My mother and I have no rental agreement other than a verbal agreement that was for me to just keep the house clean and when I was able to try and help pay what I could on the bills. The house is paid for and so there was no "rent" payment. I also buy mine and my kids own food. She draws social security and disability and her boyfriend does also. But her boyfriend has his set up that he lives in an apartment on the property, which he does not. There is no apartment on the property to live in. This past month, she decided to let two people that she barely knows move in and charged them rent of $300. She said she was renting them a room, and they were her new boarders. But there is no extra bedroom for them, so they have been sleeping on the couch in our living room and I have been trying to clean after them so my kids aren't living in a pig-style. Well, she quickly realized how messy and noisy they are and so she now wants everyone out. Including me! I have no clue how in heavens name I can find a place in such short notice with hardly no money and no job, with two kids to boot. What are my rights? I realize now, that even a parent can't be trusted. I am going to do my best to move, but I need more time. Please advise. Thank you and have a great day!