Stremme's racing roots trace to Midwestern short tracks, where his father, mother, and brother all raced before him. He claimed his first stock car victory in the early 1990s at New Paris Speedway while still fifteen years old; officials discovered his age and he was temporarily prohibited from competing. Once of legal age, he returned to the Midwestern short track scene, earning 24 feature wins, two Rookie of the Year titles, and two track championships in four years. His career went regional when he joined the Kendall Late Model Series and then national when he entered the American Speed Association, where he was named the 2002 ASA Rookie of the Year.
After signing a driver development contract with Chip Ganassi Racing, Stremme made his Busch Series debut in April 2003 at Nashville Superspeedway in the No. 1 Dodge for Phoenix Racing, finishing seventh. Despite competing in only 18 of 34 races that season, his results were strong enough to earn him the 2003 Busch Series Rookie of the Year award. He raced for Braun Racing in 2004 and FitzBradshaw Racing thereafter, posting five top-five finishes in 2005.
Stremme made his Cup debut in June 2005 at Chicagoland Speedway, driving Ganassi's R&D No. 39 Navy Dodge. Ganassi then promoted him to the No. 40 Coors Light Dodge for a full 2006 Cup season. Despite solid equipment, Stremme posted no top-ten finishes in 34 starts, with a best of eleventh at New Hampshire and Homestead-Miami. His 2007 season showed modest improvement; he started sixth in the Daytona 500 and posted his first Cup top-ten at Talladega, finishing eighth in the Aaron's 499. Following the 2007 season, Stremme was replaced in the No. 40 by IndyCar champion Dario Franchitti.
Stremme returned to the Nationwide Series in 2008 with Rusty Wallace Racing in the No. 64, running nearly the full schedule and finishing eleventh in points with five top-fives and sixteen top-tens. In 2009, Penske Racing signed him to drive the No. 12 Sprint Cup car full-time as Ryan Newman's replacement. The team lost its primary sponsor when Verizon Wireless acquired Alltel, and Stremme was released after the season without posting a single top-ten. Brad Keselowski took his seat in 2010.
Stremme subsequently attempted races with Latitude 43 Motorsports (2010), Inception Motorsports (2011–2012), and Swan Racing (2013), the latter providing him a funded operation for the full season. He was released by Swan mid-2013 and made a final run of twelve Cup attempts with Circle Sport in 2014. He has not raced in NASCAR since.
In 2014, Stremme founded Lethal Chassis, a dirt modified race car building company.
Stremme is married to Ashley Stremme, who won the Mrs. North Carolina and Mrs. United States titles in 2016. She hosts two racing radio shows — Slingin' Dirt on Motor Racing Network and Winged Nation — and won the Better Half Dash charity go-kart race at Charlotte in 2013.