Can I find out who is currently using my Airport Express speakers, and kick them?
Change the WiFi password. If I am not wrong, you can only access AirPlay speakers via WiFi. So change it and the person in question won't be able to connect. 

If you want to find out who it is, go on to your router interface something like 192.168.X.X and see who is connected. Most people name their computers, so will probably show up. Sorry if I can't be more specific.

Also, maybe there is a bug with your AE (doubt it). Maybe you should reset it.