janusgraph-java-example | Simple Java example using JanusGraph | Graph Database library

Q1: What I'm thinking is that message with defined Event Strategy cannot be serialized with GryoMessageSerializerV3d0 or Mutation Listener/Event Strategy should somehow be registered on the server side, but I can't find any references on how to do that.

That is correct. EventStrategy does not work across remote connections.

Q2: What am I doing wrong? Is it even possible to use TinkerPop's EventStrategy with JanusGraph?

It is possible to use it with JanusGraph but only in embedded mode as the MutationListener implementations do not know how to send events back to the client. The driver would likely need some significant changes to introduce a mechanism to support that so it is a non-trivial change. If that were figured out then there still remain serialization issues to sort out for users who supply custom MutationListeners (though perhaps maybe that just wouldn't be allowed).

Q3: Is there any other approach to listen to remote JanusGraph mutations?

The key word there is "remote" and I don't think anything exists currently to allow that. You would need to build you're own of some sort. One way might be to configure "g" with EventStrategy on the server and then add a MutationListener that would send those events to a separate queue that you could consume remotely. You might also consider looking at the JanusGraph Bus and devise a similar scheme.