I Have An Armstrong Oil Furnace Package Unit And The Blower Won't Shut Off After The Burner Shuts Off And It Continues To Blow Cold Air What Could Be Wrong?

Bad blower control. Usually they are called a fan and limit control. Call for service and get it replaced.

If the fan relay is bad, you can easily replace it yourself. Unfortunately on new furnaces it is part of an expensive circuit board. Post back if you want more details.