Additionally, no file with the name "ppa" exists in /usr/lib/apt/methods. Any idea what might have happened to that file, and how I might recreate it? BTW, this was after upgrading from 11.04 via the gui upgrade path.
As it turns out, the problem was related to having added the line "ppa:ubuntu-wine/ppa oneiric main" in the software sources application on the desktop and then subsequently trying to use apt-get from a terminal. Removing the line from the gui software sources application fixed the problem. Not sure where that line is stored, but it certainly wasn't in /etc/apt/sources.list.
The line "ppa:ubuntu-wine/ppa" came from the instructions on the page: https://launchpad.net/~ubuntu-wine/+archive/ppa