This is Jonathan and Darlene Edwards, the alter ego of pianist Paul Weston and his wife, singer Jo Stafford. Stafford was a "girl singer" who was famous for having perfect pitch. They created Jonathan and Darlene as a way to entertain at parties by being as absolutely bad as they could.
When asked about their connection to Stafford and Weston, Darlene said that they lived in the same house but that Stafford and Weston were "jealous because we had a Grammy and they didn't." The Grammy, of course, was for Best Comedy Album.
Please enjoy (?) and post your own favorite weird music!