Sorry, forgot to mention that. The --server option is taken in the same context as in XServer for graphical displays. That means that its the machine which will output the sound to the speakers. For the same reason esddsp is run from the machine that will transmit the sound.
It's confusing but the way to remember it is that the client makes a request (e.g. Play this wav) and the server acts on it (e.g. The sound is sent to the speakers). To avoid this problem I'll use the names esdserver (the ssh client) and esdclient (the ssh server) when talking about the sound parts.
Looking through the man pages the esdserver needs to run 'esd' with some options to allow esdclients to connect to it. '-tcp -public -port 150' should be right.
So this should work on the esdserver (I hope):
esd -tcp -public -port 150
and for the esdclient:
esddsp --server=A.B.C.D:150 -m -v
where A.B.C.D is the IP of the esdserver