This isn't WebSphere specific, but you can use a ContextListener. These listeners, which are part of a war file, get fired off when a web module is loaded onto the server. From one of these little guys, you can invoke all sorts of other Java classes.
Other approaches are to have a
Servlet configured to load at startup, and initialize Java classes in the init method of this Servlet.
Not sure if this is what you're getting at.
Alternatively, you might need to do some JACL scripting that kicks off a process or two when WebSphere starts up. I'm not a huge JACL dude, but there are some scipts that I scraped together on my website. Just follow the Carlos the JACL links.
http://www.technicalfacilitation.com/get.php?link=scripts Cheers!
-Cameron