Can I get compensation when my landlord has asked me to move out and I do not want to?

I want to know what kind of financial compensation I may have access to as my landlord has asked me to vacate my apartment in order for them to renovate it and put it on the market for over $1000 more than I currently pay. I do not have a lease and have been paying rent in full by check for 3 years. Last year the rent was raised fom 1600 to 1800, in what I believe was an effort to get me to move out as I am a student and cannot easily afford it. I have asked for written notice as I have a roommate who would also like to stay. I have been given 4 months verbal notice that I "need" to move out so they can renovate. When I asked if I might rent the renovated property should I get the resources (when I graduate I hope to get a job and could potentially afford the increase). I have also offered to let them begin renovations while I continue living there but they said that is not possible and I must move out. I have heard of people who have stayed in their apartments and stopped paying rent in similar circumstances. If I have any right to not continue paying rent for any portion of the next four months I would like to exercise them. It is going to be very expensive to move in four months as I will be unemployed and presently have no place in mind to move. Again I have no lease though I have paid rent in full on time for the past three years and have two utility bills in my name at the address.