If you look at the source of Client and Server classes, you will see they just use java.net.* package.
You can integrate the .class files found in processing-1.5.1/modes/java/libraries/net/bin/processing/net (LGPL allows to use compiled code in applications of any license) to use their functionality directly in your program.
Mmm, you also need to include core.jar, as it relies on having a reference to a PApplet. This is to register the dispose method and to get the event methods.

You can use a modified version of these classes (to get rid of PApplet), but then your code must be LGPL, I think.