If a landlord has filed an eviction in court how much time do I have to vacate?

If your landlord has properly served you with a "notice to quit" (i,e, notice to vacate the premises) and has filed for an "unlawful detainer" (i.e. eviction lawsuit), then the case will be heard in about 2-5 weeks (depending on the jurisdiction that you are in). After that, if you continue to remain on the property, then your lndlord can have a sheriff remove you. However, that typically takes another 1 or 2 weeks after a "writ of possession" is issued by the court (at the end of the eviction trial).