I don’t use MMJB anymore, I’ve switched to another program.  Do I still need MMJB, or the iPod Manager software?

No, you don’t.  You can uninstall all remnants of those programs and it’s recommended that you do.  When uninstalling MMJB, it is very important to uninstall the MMJB iPod Plugin before uninstalling MMJB.  Then uninstall the iPod Manager.  You can and should leave the iPod Software Updater program installed in case you need to Restore the iPod.