verbatim.sty file enhance default verbatim environment. It is part of TOOL package, usually you can get TOOL package with LaTeX2e macros. More details, read the document distrubited with verbatim.sty or The LaTeX Companion, please.
verbatim.el is AUCTeX's style file for verbatim.sty file. It contains definition for new commands in verbatim.sty and font-lock support for comment environment (It will work only in Emacs 21.1). If you have already made verbatim.el file by M-x TeX-auto-generate-global, then I recommend that you should remove it. Because TeX-auto-generate adds temporary command (\x) to TeX-add-symbols.
Now verbatim.el file is distributed with AUCTeX from 11.02. verbatim.el in AUCTeX 11.02 doesn't support font-lock. verbatim.patch will give you font-lock support to Emacs 21.x. It was only tested in Emacs 21. multi-line font-lock support doesn't work with Emacs 20 or XEmacs.
Now amsmath.patch and graphicx.patch are integrated to AUCTeX 11.02.
If you have some advices or claims, please e-mail to me.