Noda entered Formula One as a replacement for French driver Yannick Dalmas at Larrousse for the final three races of the 1994 season, beginning at the European Grand Prix in Jerez. Qualifying 24th behind his teammate Erik Comas, he retired from the race with gearbox failure. At the Japanese Grand Prix — his home race — he started 23rd but retired again, this time with an electrical fault. His third and final Grand Prix appearance came at Adelaide, where he outqualified his new teammate Jean-Denis Deletraz to start 23rd before retiring with an oil leak. He failed to finish in any of the three races and scored no championship points.
For 1995, Noda was lined up to drive for Simtek at the Canadian Grand Prix, but the team withdrew from Formula One entirely before he could compete. In a final attempt to secure an F1 drive, he was denied a super license, preventing him from racing for Forti at the Pacific Grand Prix at TI Circuit Aida. This effectively ended his Formula One career.
A year after his Formula One stint, Noda moved to the United States and raced in Indy Lights, where he became the only Japanese driver to win a CART-sanctioned event. The achievement cemented his place in the history of Japanese motorsport abroad.
In 2002 Noda returned to the United States for six Indy Racing League IndyCar Series races, driving for Convergent Racing and Indy Regency Racing. His best result was a tenth-place finish at Phoenix International Raceway while with Convergent.
After his American spell, Noda returned to Japan and drove a Toyota Supra for Team Cerumo alongside Hironori Takeuchi in the Japanese GT Championship. In the annual non-championship All-Star event at Aida, the pair were forced out with mechanical problems. In 1999 he joined the Esso Tiger Team Le Mans under Koichiro Mori, again in a Toyota Supra, partnered with former Australian V8 Supercar driver Wayne Gardner. The highlight of their season together was a victory at Fuji Speedway. With 33 points, they were equal seventeenth in the series standings.
In 2005, Noda was announced as a driver for the Japan entry in the inaugural 2005–06 A1 Grand Prix season, serving as second driver to Ryo Fukuda. His first race for the team came at the second round at Lausitz. In the sprint race he advanced eleven places from 21st on the grid to finish tenth, scoring one point for Japan. In the feature race he finished ninth, contributing two further points. Japan ended the season 21st with eight points total.
Noda's daughter Juju Noda is also a racing driver, having competed in the W Series, continuing a family connection to motorsport into the next generation.
Noda's career was defined by narrow misses at the highest level: he arrived in Formula One with a team on the decline, was blocked from additional F1 opportunities by licensing and team collapses, and then carved out a distinctive niche by becoming the sole Japanese winner of a CART-sanctioned race. His breadth of competition — from the Japanese Formula 3 and Formula 3000 ladder through British F3, Formula One, CART-sanctioned American racing, the Japanese GT Championship, and the A1 Grand Prix — marked him as one of the more internationally travelled Japanese drivers of his generation.