Corky was a 90s Canadian comedy band. Similar to bands like Flight of the Conchords, they would perform parodies of artists style using original material rather than spoofing specific songs. Some of Corky's humor was improvised and stream of consciousness style comedy done in very short skits.
Formed in the early 80s at the University of Windsor in Ontario, Canada's college radio station they would perform on their own show, "Last Laugh's On Us." The band's original line up was Phil Nichol, Seán Cullen, and Joe Costa but after performing in a comedy competition Joe decided to leave to pursue a career in teaching and was replaced by Greg Neale, who would cement the band's lineup for it's 10 year stint as Corky and the Juice Pigs.
During their tour in 1989/1990 The Barenaked Ladies would be the opening act for Corky, later going on to huge success on their own as humorous band. Touring was the band's life for much of their early years, it took until 1992 for them to release their first album, the casette only "Buck a song." The casette would have many of it's tracks reprised on their next album, which was also much more widely available.
In 1993 they would followup with their self title album, performing most of the same songs, a few new ones and some new transitional skits. This album would contain their biggest hits that would be made famous later on and contained the song that is likely their lasting legacy. Eskimo has often be missattributed to other artists, including the king of parody himself, Weird Al.
1994 would be their followup album, Pants, which featured higher quality production. While I enjoyed the album a bit I personally find their first one a bit stronger in terms of songs.
Much of Corky and the Juice Pigs fame came in the form of their appearances on the American sketch show MadTV in the mid 90s. Corky was the first musical guest on the original 90s MadTV and would regularly perform on the show right up until their break up.
While producing new music in 1998 the band's label, Denon, closed it's doors. For whatever reason, Corky decided to call it quits then. Seàn Cullen and Phil Nichol moved on to fairly successful comedy careers. In 2014 Nichol released his first new material since the dissolution of Corky and The Juice Pigs, the project is named Late Night Electric Watermelon and it can be downloaded via Band Camp, if you're interested. Cullen appeared on Last Comic Standing back in 2008 and starting in 2012 became a regular on the Match Game game show. As for what happened to Neale? Nobody knows, he faded off into the sunset.
Two of the songs that were written before their breakup are only available via their appearance on MadTV.
Phone Sex Girl seems hard to find, I can only find this low quality version of it under the guise of an AMV.
You can easily blow through all of Corky's discography in two and a half hours if you are interested. All of the albums are available here on youtube under playlists https://www.youtube.com/channel/UCFqc4wSjDic08yWrPJ831VQ/playlists
I really think that @weslikestacos band would do a great cover of these two songs:
UPDATE: I just looked at the credits for Phil Nichol's album, Electric Watermelon, and it appears that Corky ALMOST lives on. There are two songs that are credited as having been co-written by former bandmates. "H.A. Cowboys" is credited to Cullen/Nichol/Neale, which you might recognize as the entire lineup of Corky and the Juice Pigs. "ECG" is credited to Nichol/Neale.