The ScriptEnginePlugin allows the use of any of the engines on scripting.dev.java.net to be used inside the jEdit plugin context. It also provides two utility-like methods for executing the buffer or the currently selected text.
ScriptEngine selection and execution is edit-mode based. This means that to run a Groovy script, your jEdit mode needs to be set to "groovy".
Documentation for using the utility methods, and integrating your own ScriptEngine comes with the ScriptEnginePlugin help files.
I've also been working on getting a patch included in jEdit which allows you to hit CTRL+SHIFT+N to get a new file in a chosen language. This new keystroke opens up a dialog listing all the languages jEdit can handle. You can then select a language, or use shortcut keys to get your language of choice (eg. 'x' gets you XML).
Anyway, if you have some time and are a jEdit fan, please check them out. I promise to get right back on the Platform game now. :)