cannot get rid of adobe reader update pop up and I have no adobe reader installed

Check the Utilities folder inside your Application folder. There you will find various Adobe utilities, which are probably at fault. You can turn off the updater or delete the offending apps.

Depending on how you uninstalled the app, you may have remaining app "remnants"

Reinstall the app and use Adobe's instructions on complete removal. Or use the safe free app AppCleaner.