On Mac OS X I find that jEdit does not respect the "preferred" JVM setting. It seems to always use the Apple 1.6 JVM.
I am using jEdit v4.5.2, on Mac OS X v10.8.1.
1) Use "Java Preferences" from "/Applications/Utilities", to change the the preference order for your installed JVMs. I have installed Oracle Java 7 and moved this to the top.
2) Verify this setting has taken hold by running "/usr/libexec/java_home" from a terminal window. Here's what I get:
jam:~ % /usr/libexec/java_home
3) Open jEdit, and go the "About jEdit" window to see which JVM is being used.
Other Java applications (such as NetBeans) respect this preferred JVM setting, as should jEdit.