Is there a way to run JNode, and our own OS, on the Raspberry Pi?
I'm not sure about Jnode, but the Computer Laboratory at Cambridge University has a short course on OS development on the Raspberry Pi that you might be interested in:
You are in for a lot of pain if you go the Java way. Also operating systems capable of actually doing anything interesting takes much more work than you most likely think.
JNode requires as of now more memory than the Pi has and is not ported to the Raspberry, so it will require quite a bit of elbow grease to get up and running.
You might find it much more rewarding in terms of actually getting the computer to do something, to do some work on completing driver support on the Linux distribution you end up using. Raspbian seems to be where the momentum are these days.