I'm confused: your title says "delete variables" but the post asks about "editing variables".
If you are trying to edit the variable definitions in a number of documents, edit the variables in one file, and then use File > Import Formats to import the updated definitions from the edited file into the other files.
As for deleting formatting from multiple files—whether variables or para formats, char formats, master pages, etc.— this is not a strength for FrameMaker. Use File > Import > Formats to add formatting, but you'll need to look into a 3rd party app to remove formatting from multiple files at one time. I've used Finalizer by Squids (Basic package for FM ) in the past and while expensive, it greatly automated the clean up.