The CD album artwork was created by Masahiko Ohno; three different color variations were released, with each corresponding to either Japan, North America, or Europe.

While Shonen Knife's usual sound is Ramones-inspired pop punk, the band branched out musically and listened to harder rock bands for Overdrive, such as such as Bad Company, Black Sabbath, Boston, Deep Purple, The Doobie Brothers, Judas Priest, Thin Lizzy, and ZZ Top—for inspiration.

Because of the band's exploration, the album's name references the overdrive pedal, which, in Yamano's mind, conjured up images of 1970s rock music.

She revisited this opinion after watching a tennis match on television in which the announcer referred to a move made by Kei Nishikori as a "great jet shot".

"[7] Will Fitzpatrick of The Skinny awarded the album four out of five stars, writing that "Overdrive's sugary take on 70s dinosaur rock" is replete with a "never-ending supply of bubblegum hooks".

[8] Mark Deming of AllMusic awarded the album three out of five stars, commenting on the band's musical shift; he wrote, "By Shonen Knife's standards, Overdrive does sound like some sort of hard rock album, and the attempts to make like Kiss, Thin Lizzy, or Deep Purple come off better than one might expect, though Yamano's guitar skills are less impressive than those of the average metal axe slinger.

"[10] Deming complimented the charm of the album, but criticized Yamano's lyrics as "run-of-the-mill", ill-fitting the change in musical direction.

However, he was slightly critical of the "derivative" nature of the band's sound, as well as their "one-dimensional guitar playing and unrelentingly trivial lyrics".