If I am paid up on rent, can my landlord give me 30 days to move without an eviction notice?

If you don't have a lease then you are at best a month-to-month tenant. That means even if you are doing everything you are supposed to be doing, the landlord can give you a 30 day notice to terminate your tenancy. If you don't leave in 30 days landlord can initiate eviction action after 30 days has passed since notice. Since you have no rights without an occupancy agreement you most likely will ultimately unless you can show an agreement that gives you more rights.