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Female empowerment is the name of the game in “Lady Mechanics,” a shaggy but good-hearted musical at Annoyance. Featuring a book by Michelle Renee Thompson and Wolfgang Stein, with a nifty little score by Greg Szydlowski, the show draws inspiration from the real story of Sandra Aguebor-Ekperuoh, the first female mechanic in Nigeria who claims that her vocational calling came to her in dreams from God. (Vernon Mina plays the bewigged, bearded and guitar-toting Jesus here with understated aplomb.)

In this show, directed with a mix of affection and indifferent stagecraft by Stein, Sandra (Thompson) has to whip a trio of her fellow countrywomen — a rural bumpkin (Angela Oliver, delightfully assured), a rich teenager (Brandi Denise) and a sassy sex worker (Aasia Bullock) into shape as top-flight mechanics. When her ex-boyfriend, Reginald (Warren Phynix Johnson) shows up with a busted-up taxi, a pair of clueless American tourists and a gun, the stakes get higher.

Or at least they should — but despite the oodles of charm on display here and some truly catchy musical numbers (including the anthemic “Change Your Oil”), the story itself doesn’t really explore and deepen the connections among the characters. There is a lot of great human comedy and drama to be tapped from illustrating the lives of women in a troubled region fighting back with wrenches and moxie against oppression. Both Sandra’s story and the show deserve further development.

Through Aug. 3 at the Annoyance Theatre, 851 W. Belmont Ave.; $20 at 773-697-9693 or annoyanceproductions.com.

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