Giving Section 8 Notice to Leave

[Michael Cavicchi]

So I haven't been the best 'landlord' or 'investor' so to speak.  I currently live in my own three family house.  I have been renting to tenants since I have owned it, October 2017, that happen to be section 8.  Due to the fact that I would like to get into that side and renovate, I decided I was not going to renew their lease when it ended Aug. 31st.  I gave them notice (verbally and through letter) of this back in April because they have kids and I was trying to be nice about it. 

To be fair, they have been looking (confirmed by housing authority), but they did not find a place by the end of their lease (I won't get into the obvious reasons why).  Housing authority needed me to say it could go month to month so that I could receive the money despite it saying so in the lease.  

I am trying not to have this drag out forever and Housing Authority told me just give them a date.  After that it's up to me to evict them.  I'm thinking of saying I need them out by Jan 1st.  Is there anything I need to be aware of in this? If they stay past that date and I start eviction proceedings do I not get the rent at that point? Is there any obligation on my part to let them stay because it will be mid winter?