"Jashin-chan Dropkick" centers on Yurine Hanazono, a college student who accidentally summons a demon girl named Jashin-chan while performing a ritual. Jashin-chan, a snake-like demon from the underworld, is bound to Yurine and attempts to kill her to return to her realm. However, Yurine proves to be exceptionally resilient, often thwarting Jashin-chan's murderous schemes with ease. The two form a contentious cohabitation, with Yurine treating Jashin-chan more like a nuisance than a threat.

The series adopts a comedic and episodic structure, focusing on the absurd and chaotic interactions between Yurine, Jashin-chan, and other supernatural beings. Among these characters is Medusa, a gorgon who becomes Jashin-chan's rival and later a reluctant ally. Medusa's presence adds to the series' humor, as her attempts to outshine Jashin-chan often backfire. Another key figure is Pekola, an angel sent to monitor Jashin-chan, who frequently finds herself caught in the crossfire of their antics. Despite her divine mission, Pekola is often portrayed as naive and overly trusting, contrasting with the more cynical personalities of the other characters.

The narrative frequently explores themes of coexistence and unlikely friendships, as the characters navigate their conflicting natures and goals. Jashin-chan's persistent failures to kill Yurine become a running gag, highlighting the series' comedic tone. The manga also incorporates elements of mythology and folklore, reimagining traditional figures like demons, angels, and gorgons in a modern, humorous context. The dynamic between the characters drives the story, with their interactions ranging from slapstick comedy to moments of unexpected camaraderie.

As the series progresses, additional characters are introduced, including Minos, a demon who serves as Jashin-chan's underworld contact, and Poporon, a demon girl with a crush on Yurine. These characters further expand the chaotic world of the series, contributing to its unpredictable and lighthearted atmosphere. Despite the frequent comedic tone, the manga occasionally delves into the characters' backstories, providing glimpses into their motivations and vulnerabilities. This balance of humor and character development ensures that the narrative remains engaging while maintaining its comedic core.