The series follows the exploits of Odd Squad, an organization run entirely by children, that solves peculiar problems using math skills. In particular, it typically features two employees of the organization's investigation division that work in precinct 13579 of the organization—Agents Olive (Dalila Bela) and Otto (Filip Geljo) in the 1st season, and Olympia (Anna Cathcart) and Otis (Issac Kragten) in the second season. Selected episodes feature other types of employees of the fictional organization, like security officers, so-called "tube operators", and scientists. The names of the employees, with one exception, always start with the letter O.
Agents are typically assigned cases by their boss, Ms. O (Millie Davis), and travel via a system of interconnected tubes to get to their destinations. They deduce the solution to the problem or how to detain the perpetrator by using basic mathematical principles that are typically the focus of the episode. Often, they cannot solve the problem at the scene and must go back to their precinct's headquarters or to the "Mathroom" (T.J. McGibbon), a sentient space that communicates through large paper fortune tellers and can unfold them to display information to help the agents see connections and better solve their case. Along with math, agents also use "gadgets" designed by the scientists; in the first season, Agent Oscar (Sean Michael Kyer) heads the lab, gaining an assistant, Agent Oona (Olivia Presti), in early season two who eventually takes over the lab. The characters also have to deal with a variety of recurring villains who often put a mathematical spin on their plots.
The seal of the Odd Squad headquarters depicts a jackalope carrying a shield in front of it (bearing an image of the seal—an instance of the Droste effect) and bananas at each side of it.