"Oyako Club" centers around the lives of parents and their children who gather at a local community center to share experiences, challenges, and joys of parenting. The narrative unfolds through a series of episodic vignettes, each focusing on different families and their unique dynamics. The main characters include a diverse group of parents, ranging from first-time mothers and fathers to seasoned veterans, as well as their children, who range in age from toddlers to pre-teens.

The series explores various themes related to parenting, such as the struggles of balancing work and family life, the pressures of societal expectations, and the emotional highs and lows of raising children. Each episode delves into specific issues, such as dealing with temper tantrums, navigating school pressures, or managing sibling rivalries. The parents often seek advice and support from one another, creating a sense of community and camaraderie.

Key characters include a single mother juggling her career and her young son, a stay-at-home dad adjusting to his new role, and a couple dealing with the challenges of raising a child with special needs. The children, too, have their own storylines, highlighting their perspectives and experiences as they grow and learn.

The series balances humor and heartfelt moments, offering a realistic portrayal of family life. It emphasizes the importance of communication, understanding, and mutual support among parents and children. Through its relatable scenarios and well-developed characters, "Oyako Club" provides an insightful look into the complexities of modern parenting.