Updated info.....

I went to the Build Path Properties in eclipse, Order and Export tab,
and checked the 2 jars.  I also had to manually add them to my System
CLASSPATH.  That took care of the the ClassDef errors.

However, the external jars use some native code and a DLL in the
C:\WINDOWS folder, and now I am getting an UnsatisfiedLinkError on one
of the native calls...

Again, it all works fine in eclipse.  So now I am even more confused

Any ideas?

During the Export process, there is an opportunity to let you decide if
you want to export other project(s) into the destination jar file. It is
a thing of check or un-check. In terms of those needed jar files, I
don't remember. I guess they are similar situation as the needed projects.

If my Eclipse project needs other project classes to work, I can export
all of them into a big jar file. Or I can only export my Eclipse project
into a smaller jar file, but I need to add those needed classes' paths
into classpath variable.

Yes. Like I said previously, pay attention to each step when exporting,
there is a check or un-check thing to let you decide.