To test for a draw you need to properly set up your meter to measure amperage, not voltage. Disconnect the negative cable and put one probe on the negative post and the other on the negative cable and this will give you a readout of how many amps the car is pulling. Use alligator clips and then let the car sit there a while to let all the modules go to sleep. Ensure the doors are all closed and the key is out of the car.
However your issue just sounds like a bad battery. The fact that the voltage is visibly falling while the battery is out of the car means its just unable to hold a charge.