My avanti thermoelectric compact refrigerator periodically runs very loud which is not normal. If I hit it, it stops and runs quietly again. Any ideas? I have already cleaned the dust off thoroughly and ensured that the appliance is level.

The noise if from a sympathetic vibration of the unit which transforms to vibrate any loose joints, parts or fittings.
You will need to listen to the noise, use your hand to hold up the plastics or the joints in the bottom section of the unit or the frame work. It will require a lot of patience to find the source of noise. Pad it up after tapping for loose noise on the rear and insulate the noise heard till you finally get rid of any vibration noise..