I used emacs, with hex mode that shows the characters in the file as hexadecimal strings. See http://www.gnu.org/software/emacs/. The "hexl" major mode is standard with emacs, no additional packages are needed. Note that emacs is not for the faint of heart, though--it's a powerful editor, but it has a famously steep learning curve.
As for getting rid of the character in the source XML, if they are static files, you should be able to just edit them out in the usual way. (In Epic, you can use Find entity to search for "nbsp", and replace each instance. Or you can just paste the character in the normal Find/Replace dialog.) You could also write a pretty simple Perl script to do the replacement.
If the XML is coming from a CMS or database, you'll have to figure out a way to modify the contents of the system, or at least to modify the output pipeline to strip out the 's before serving the content.