Do you just want to run class files that just so happen to be bundled in the WAR, or do you want ot interact with the actual, running WAR instance? If the former, then the WAR is just a normal Jar file and you can execute classes in that just like any other other Jar file.
If you want to interact with the running WAR, then you might want to look at JMX.
All current JDKs (at least 1.5+) come with JMX "for free". It's easy to create little interface classes to be used as commands to interact with your WAR.
THen you would need to create a command line program that connects to the WAR via JMX, or you can use a tool like JConsole (which comes with the JDK, but it's a GUI) to interact with your instance. There are other JMX clients out there as well.
If none of that is attractive, there's always web services.