[2] During the Gators' run in the 2005 College World Series, O'Day made four relief appearances and earned a save.

He was designated for assignment by the Mets two weeks into the season in order to make room on the roster for Nelson Figueroa.

[3][4] The Texas Rangers claimed him on April 22, 2009 and he made his debut the same day in extra innings against the Toronto Blue Jays, just minutes after getting to the bullpen from the airport.

Limited to sixteen appearances due to a pair of injuries, O'Day was 0–1 with a 5.40 earned run average (ERA) in 2011.

He also pitched in eighteen minor league games with the Frisco RoughRiders and Round Rock Express, going a combined 1–0 with a 2.53 ERA.

[6] During this period, when he arrived at the mound, Texas Rangers' fans began a traditional chant of his last name.

Following the struggles of Pedro Strop, O'Day settled into the role of the 8th inning setup pitcher later in the 2012 season, often leaving the game in a manageable state for closer Jim Johnson.

Former Orioles reliever and fellow submarine pitcher Todd Frohwirth worked with O'Day during spring training in 2014 to improve his change-up.

He set career-bests in innings pitched, saves, ERA, WHIP, strikeouts, and opponent batting average.

O'Day also appeared in the Wild Card Game for the Orioles, tossing 12⁄3 innings while striking out one batter in a 5–2 loss.

[11] On July 31, 2018, O'Day, along with Kevin Gausman, were traded to the Atlanta Braves in exchange for Brett Cumberland, Jean Carlos Encarnacion, Evan Phillips, Bruce Zimmermann, and international signing money.

[12] O'Day opened the 2019 season on the injured list with a right forearm injury, which followed a single spring training appearance.

[20] On May 1, O'Day was placed on the injured list with a right rotator cuff strain,[21] and was activated on June 29 after a near two-month stay on the IL.

[25] While rehabilitating the injury in the minor leagues, O'Day sprained his right big toe and was transferred to the 60-day IL in September.

His paternal grandmother, who had raised his father Ralph and two uncles on her own after his grandfather died in a car accident, shortened it to Odach (the "ch" is silent in Polish phonology) to make it easier to pronounce for her colleagues at Montgomery Ward in Chicago.

[citation needed] In 2017, O'Day was honored as the 2017 Major League Baseball recipient of the Bob Feller Act of Valor Award for his work with the United States Military.