I have a heat pump with central air and electric heat options. The thermostat is off and the fan is off but I have air constantly blowing from all vents. Why and how can this be happening ?

If the blower is running then it should not be with everything turned to off.

If you have an electric furnace the problem could be

A defective heat sequencer
A defective fan blower relay.
Improper or shorted thermostat wiring

You will need to track down the problem with a meter.
The wiring diagram is located on the inside of the blower access door on the inside unit.