The series follows the exploits of Odd Squad, a kid-run organization that solves peculiar problems using math skills. In particular, it typically features two investigation agents 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 groups of agents at the organization, like security officers, tube operators, or scientists. Agent names always start with the letter O.
Agents are typically given cases by Ms. O (Millie Davis) and travel through a tube system to arrive at the scene. They deduce the solution to the problem or the perpetrator of it using 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 talking room that can display their information in front of them to help them 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. Agents also face off with a variety of recurring villains who often put a mathematical spin on their nefarious plots. Even though they occasionally arrive at a point when they believe the case is unsolvable, the agents always end up finding a solution to the problems.
- Agent Olive (Dalila Bela, season 1): A veteran agent of Odd Squad, Olive began season 1 adapting to working with and training her new partner, rookie agent Otto. Olive is usually calm, brisk, and serious. She has a morbid fear of pies, which she acquired after saving Odd Squad HQ from a pie-related disaster instigated by her previous partner, a very gifted agent named Todd who was removed from the squad and became a villain. In the season 1 finale, Olive departs the series along with her partner, Otto, to run a different Odd Squad precinct as Ms. O.
- Agent Otto (Filip Geljo, season 1): Olive's partner, and in the opening episode the newest Odd Squad agent. The fun-loving Otto acts as a comic foil to Olive's straight-man demeanor, frequently annoying her. Although a rookie, Otto frequently uncovers the facts needed to solve the case at hand, even doing so in Olive's absence, proving his worth as an agent. In the season 1 finale, Otto departs the series to run another Odd Squad office as Mr. O with his partner, Olive.
- Ms. O (Millie Davis, seasons 1–): "Ms. O" is the title of any female head of an Odd Squad division, but in-show, the title most often refers to the head of the division featured on the show. The stern Ms. O leads the organization with an iron fist. She has the tendency to yell (a habit seen less frequently as the series progresses) and is often seen sipping a juice box. Despite appearing younger than most of the agents, Ms. O has worked for Odd Squad for several decades; her actual age remains a mystery. Before she became Ms. O, she worked as an Odd Squad field agent, going by the name "Oprah".
- Agent Oscar (Sean Michael Kyer, seasons 1–2): Odd Squad's resident scientist and gadgeteer, Oscar is a quirky though incredibly knowledgeable genius who spends most of his time at Odd Squad Headquarters tinkering with gadgets in his lab. Agents go to him for technical solutions to their problems. Oscar has a goofy side, delivering his zany scientific rants with a generous dose of hand gestures and vocal sound effects. Oscar departed from the series in the episode "Oscar Strikes Back", where he became the president of the Odd Squad lab sector after the former president was removed from Odd Squad for misconduct.
- Agent Olympia (Anna Cathcart, season 2): A new agent, introduced at the start of season 2, who joins to fill the opening left by the departure of Olive and Otto in the season 1 finale. She was given early graduation from the Academy because Ms. O wanted her in the equivalent of Otto's position.
- Agent Otis (Isaac Kragten, season 2): A new agent, introduced at the start of season 2, who joins to fill the opening left by the departure of Olive and Otto in the season 1 finale. He is generally very serious and does not like to speak. There is no record of him attending the Academy, but he is the seasoned member of the new team. He exhibits dislikes others around him find strange, including an initial distaste for gum and a dislike of the ingredients of pizza when offered a pizza party for solving 50 cases in a week.
- Agent Oona (Olivia Presti, season 2): Odd Squad's resident scientist and gadgeteer. Oona took Oscar's role as the lab scientist in Odd Squad headquarters after the events in the episode "Oscar Strikes Back".
- Dr. O (Peyton Kennedy, seasons 1–): The head doctor of Odd Squad. She is known for her eccentric behavior and frequently says things that make no sense, whilst frequently reminding the agents "I'm a doctor!" in a manner reminiscent of Star Trek's Dr. McCoy.
- Agent Obfusco (Jaeden J. Noel): An Odd Squad agent and cross-cultural expert who speaks in obscure riddles. He is difficult for the other agents to understand, and extremely peculiar, even for an organization named Odd Squad, so the other agents try to avoid working with him. He has a sister named Obfuscolina who is even odder and is hard for even him to understand.
- Agent Ocean (Elijah Sandiford, season 2): Odd Squad's director of the creature room. Ocean has a laid-back and easy-going personality and he is friendly to the other agents. He specializes in animals/creature knowledge that Odd Squad agents may need to know.
- Agent Octavia (Julia Lalonde): Agent Oz's partner. It was noted in an episode that she is one of Ms. O's best agents. She is usually looking for Agent Oz because he is invisible.
- Oksana (Madeleine Barbeau): Odd Squad's resident cook, who prepares all the meals by herself. She has a deadpan manner.
- Agent Olaf (Eshaan Buadwal, seasons 1–): Agent Oren's partner. Olaf is happy-go-lucky and jovial in nature but tends to be very simple-minded. Despite this, he has shown to have moments of intelligence, often to the shock and amazement of his fellow agents. He shares Oren's penchant for laziness. He dreams of becoming a dentist and fears not becoming one. He loves potatoes. It is later revealed that he is a werewolf.
- Agent Orchid (Michela Luci, seasons 1–): One of the younger agents. She tends to be extremely stubborn.
- Agent Oren (Brendan Heard, seasons 1–): Agent Olaf's partner. Oren is snarky and arrogant. Oren and his partner have an ongoing rivalry with Olive and Otto. Unlike their industrious rivals, Oren likes to weasel his way out of work whenever possible. Oren likes to brag and considers himself Odd Squad's best agent. Oren has a fear of pancakes and dreams of becoming director of Odd Squad.
- Agent Owen (Christian Distefano, seasons 1–): The head of Odd Squad security.
- Polly Graph (Ava Preston): A girl who runs a stand selling hot chocolate or lemonade, depending on the season, outside her house. Odd Squad agents frequently patronize her stand. She is very fond of graphs and always has just the right visual representation to deal with the situation at hand. While she is not an agent, she offers data of all sorts to agents passing by in town. Ms. O has asked her to come in to assist on cases and internal business within the squad on occasion.
- Sound Check (Lucas Meeuse, Matthew Armet, Thomas Alderson, Stephan Dickson): Fictitious and satirical boy band made up of Tony D., Danny T., Ringo, and Johnny J., and is well liked by all the Odd Squad agents with the exception of Agent Olive, who later admits to liking them in Odd Squad: The Movie (2016). Songs by the group include Take Away Four, The Force of Gravity and Up, Down, Left, Right. Sound Check as a group appears on the album Odd Squad: Stop the Music by Paul Buckley (PBS Kids, 2016).
- Flatam (Martin Roach, seasons 1–): A villain who converts objects and people into a two-dimensional form.
- Odd Todd (Joshua Kilimnik, seasons 1–): Previously an agent at the squad, Todd was removed from the squad for causing problems and subsequently became Odd Todd. A recurring villain in the first season, he was outsmarted by Agent Otto and renounced oddness for other interests. In the second season, he has taken up gardening and has been seen providing assistance to agents at the squad. Early in the first season before Todd was introduced, it was a running gag that characters would comment about Otto being "so much better than Olive's last partner." Upon Otto's asking about who was her last partner, they would change the subject.
- Shapeshifter (Laura Landauer, seasons 1–): A villain who can transform or transform anything into another thing but remains the same weight.