The band members claim the name came when Brennan asked Drake, in a town somewhere on the BC coast, "What are the odds of us ever escaping bullshit gigs like this?"

In 1991 they released their debut self-produced album Neopolitan, which spawned the radio hits "Love Is the Subject" and "King of the Heap" (both sung by Northey).

"Jack Hammer" features a guitar battle between Robert Quine (Lou Reed, Richard Hell, Matthew Sweet, etc.)

The follow-up single "Make You Mad" featured a video which was co-directed by and starred Bruce McCulloch of The Kids in the Hall.

The band performed until 1999, headlining that year's Arts County Fair year-end concert at the University of British Columbia, but released no further new studio albums.

In March 1999, Northey announced that he was leaving the band, although he continued to work with Elliott and Steward frequently in subsequent years.

Later in 1999 Elliott, Steward and Northey teamed up with organist Simon Kendall (of Doug & the Slugs) to release an instrumental soul CD under the moniker Sharkskin.

Drake followed up his previous work mixing The Tragically Hip's 1996 album Trouble at the Henhouse by furthering his career as a recording engineer and producer based in Vancouver.

Northey released a solo album, Giddy Up, in 2002, and worked as a songwriter and producer for other acts (including Rosanne Cash) throughout the decade.

Northey, Steward and Elliott all recorded and toured with Rob Baker of the Tragically Hip as the band Stripper's Union, and continued to perform as the Craig Northey Power Trio, in addition to forming the core of the backup band for Canadian blues-rock guitarist Colin James.

A new EP, Noise Trade (named for the website used to sell it), comprising several songs from Cheerleader and covers of tunes from Pointed Sticks and Art Bergmann was prepared for early 2009 release.

Early in the year, the band also appeared as themselves (in retro-'50s garb) during a dream sequence in the final season of the Corner Gas television series.

On December 3, 2021, Odds were mentioned in the song "Canada Loves You Back" by Steven Page, which he performed at the Governor General's Awards in honour of Ryan Reynolds.