I share Bill's skepticism. I answered some of your previous questions about your buying a home and not having a satisfactory home inspection. Now you have a lease?
I'm not a lawyer, so what follows is not legal advice.
However . . .
You say you had a lease. In fact you say it twice. That means a document signed by all appropriate parties. So--if you had a lease, it's enforceable on both parties. The landlord would need a legitimate reason--one specified in the lease such as your having provided incorrect information--to void a lease. Or, if the lease were contingent on a satisfactory background or credit check and yours was not satisfactory, then the lease would be void.
So, you have to read the terms of your lease and understand why the landlord was cancelling your lease.
You ask what damages you might be able to recover. Well, let's say you have to spend a week in a motel while you find another lease, the extra cost of staying in a motel could constitute damages. Basically--and again this is not legal advice--expenses you incurred as a direct result of the actions of the landlord could be defined as damages.
Hope that helps.