Rob,
I’m not sure why you had a JRE subdirectory under the MyEclipse subdirectory, but I’ve not seen that before. The only thing you should need to change (if it didn’t update automatically) is your “Installed JREs” setting in Window->Preferences->Java. If you are doing web app development, you will need to set this JRE to your JDK path and not a JRE path.
I’m confused why your user.dir is resolving to the JRE directory. I’m not aware of any side effects this may cause, but I’ve also never encountered this before. If you wanted to be absolutely safe beyond a shadow of a doubt you could uninstall everything, reboot and reinstall everything; but I can’t promise that will fix the user.dir issue.
Can you check your environment variables (Windows Key+Pause) and see if maybe there is a strange var in there causing the user dir to resolve to the JRE dir?