Vintage Synth Repair

Things don't buzz when turned off.  The problem has to be downstream
from the Ody.

You've possibly got a ground loop between the Ody and your PA.  Swap
the audio cable with a known working one and see if that improves it.

Also try plugging the Ody into a completely different household
circuit.  If two units with a bad ground are plugged into the same
side of the 3-phase supply, you can get ground hum.

Finally, take the Ody over to a friend's house and plug it in there,
with his audio cable and see if things are different.