An odd number was any number not evenly divisible by two.
In 2267, James T. Kirk described the last time he had seen Areel Shaw as having been "four years, seven months, and an odd number of days" ago. (TOS: "Court Martial")
Later, Janet Wallace described the last time she had seen Kirk as having been "six years, four months, and an odd number of days" ago. (TOS: "The Deadly Years")
In 2372, Captain Benjamin Sisko ordered odd numbered launchers to fire. (DS9: "The Way of the Warrior")
In 2373, while sharing quarters on Deep Space 9, Nog suggested he clean up on odd numbered days, while Jake Sisko do so on even ones. When Jake expressed his surprise that they would be cleaning every day, Nog, clearly confused, replied that they would only do so on odd and even days. (DS9: "The Ascent")