Am I responsible for damages or cleaning if there is no rental contract?

There is a lot of issues at my current home. I am renting from my soon to be ex-husband's family. He lived in home with me for 4 of the 5 years that we have rented home. We never signed any agreements with family members. In fact all utility bills are in her name. He has left several messes in yard that I am unable to clean up. He also has broken kitchen cabinets. I cannot make these repairs. Not to mention the fact that the landlord has refused to make many reapirs around the home, including a broken toilet and also a frog infested swimming pool with a broken water pump. I am moving and I have been getting harassing phone calls and threats from landlord that I have to fix items before I move or she will sue. Can she legally sue me? I have never signed any agreements with her and she has not reapired anything in the home while I was living there. I have never missed a months rent or been late.What should I do to protect myself?