Can your landlord ask you to leave?

I sub in the school system in a city in NC and the month of June,July and August now it's pay put sometimes late. Now the problems that I have is even when th rent is paid on time things that she knows need to be done has not and and it seems all she want is the rent. My kids and I have no smoke detector, the deck and the steps leading out of the back doors are very bad and unsafe, the roof on the house is so bad the we have water spots on the ceiling in the baths-master bedroom and in the kitchen. No gutter on the back of the house and the one on the front is very lose on the left side on the house. The house came with central air and heat but never worked, the dish washer work but leaks water so bad that we don't use it. There are sockets throughout the house that does not work. She put a window unit in the window in the front part of the house but this is a three bedroom and a 1 bath and 1/2 and it has not been serviced since it was put in about 4 years ago and I just replaced the ceiling fan in the master bedroom after about 4 years and my daughter and I have asthma. Now you may say why are you still there but the way the economic is I just can't afford to move I just keeping my head above water with a 24 and 20 year old kids in college. What can I do or better yet can I do anything about this. Because if she does tells us that we have to move out we have NO PLACE TO GO. We need help. can you help us?