Schedule an appointment with a landlord tenant lawyer to pursue a wrongful eviction case and breach of warranty of habitability case for the flood and lack of heat.
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Do you have a lease? If no, you are a month to month tenant and the landlord can evict you through the court but the landlord cannot collect unpaid rent on an illegal apartment so if you stop paying the landlord won't be able to collect the back rent while the case moves through the system. You may also have a constructive eviction case. The above may give you some leverage if you try to negotiate something with the landlord.
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In New York, an email notice to terminate tenancy may not be proper, and so, if the landlord does not follow up with a formal written notice, the failure to properly terminate the month to month tenancy is a defense in the summary proceeding. If the landlord cannot prove making a proper termination notice, the court may dismiss the lawsuit.
Outside New York City a landlord is allowed to terminate a month to month tenancy with a "One Month" (not thirty day) notice and that is significant, as months are not equal in number of days. A termination notice served on a tenant in May 2013, will not be proper unless at least one month notice is provided and the notice acts to end the tenancy on June 30, 2013 (not a day earlier or later, if your rent due date is the first day of the month.) Again, a notice of termination not properly made should result in a dismissal of the landlord's summary proceeding based on that notice.
Your landlord has committed at least three illegal acts and you should look to a financial recovery. First, your landlord rented an illegal dwelling. That act is prohibited by law, but New York has not created a statutory right for the tenant to "clawback" rent payments, innocently made by the tenant, so the tenant is forced to affirmatively sue the landlord for fraud, illegal contract, breach of lease, and similar grounds that you and your attorney may rely on to try to get your paid rent money returned.
Second, your landlord committed a breach of lease (a breach of the warranty of habitability) by shutting off your heat. A court may consider that wrongful act of the landlord is a form of illegal eviction, and that may also allow you to recover money damages.
Third, your landlord allowed you (in your illegal apartment) to be flooded out. Again, that is a fact that may support a claim for a breach of lease and a constructive eviction.
New York forces tenants to battle for rights against landlords who willingly violate law and local code and rent illegal dwellings to innocent tenants, so hiring an attorney to fight for you is important.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.