HVAC making sound even when off
Sounds like contactor chatter. Could be a bad contactor, or not enough power on the coil.

Basically, the contactor is closing and opening really quickly.  This happens when the coil doesn't create a strong enough magnetic field to hold the contactor closed. 

Depending on the cost of a new contactor, I'd probably just pop in a new one. If it doesn't fix the problem, you'll have to troubleshoot further. If you have (or can find) the manufacturer's specifications for the contactor, you could measure the contactor coil resistance and compare it to the spec.

You can also check the voltage of the control wiring going to the contactor coil. 


Remove the low voltage wires from the contactor, and position them so they do not come into contact with each other or anything else.
Set the thermostat so that it's calling for cooling.
Use a voltmeter to check the voltage between the two low voltage wires.


You should measure about 24 volts (assuming it's a 24 volt control system).