There is the urban version of shoot shovel and shut up, perhaps a
little creative vandalism is in order although I would consider it a
last resort as you don't want to start a war.
What worked for me was to play the same music delayed a bit. Or in the
case of radio to tune a little off the station and send some noise on
back.
Perhaps deer can be trained to eat speaker wires.

On the topic of deer they will not walk on chicken wire. It goes up
between their toes and they do not like it at all.