I have an Intertherm furnace and a/c unit.The problem is neither will shut off unless physically turned off at furnace.Theres also an heat,off,a/c switch on thermostat and I hear a relay clicking in furnace when I move this switch back and forth on the thermostat but to no avail, the furnace stays on or the a/c stays on when switched to that mode on furnace.

Does the furnace heat or the A/C outside unit keep running or is it just the inside blower that keeps running?

Yes the furnace blows hot and the a/c blows cold continually.I even disconnected the tremostat and they run nonstop

You have a problem with the low voltage side of the system more than likely. It could be a short in the thermostat wiring in a wall or in the furnace. I would sound out those wires first then move on to the rest of the 24 volt components like relays etc.

If your unit has a A/C/OFF/FURNACE switch in the furnace like some mobile homes have the problem could be a shorted switch or the relays it controls.