My heater and air unit keeps blowing cool air off and on at weird times of the day... Even when off. We have to go out and turn off power to unit to get it to turn off. What could cause this?

With out knowing the information of your system (make and model) it's a stab in the dark. If the blower runs all the time with no heat it sounds like a limit switch has tripped. The control board on the system should have a flashing light letting you know what the fault is. Count the blinks of the light or lights and the code for faults should be on the blower door.

Our unit is a Trane XL1200