Onidi began his single–seater career in 2004 in the Formula BMW ADAC series, as one of current Formula One driver Sebastian Vettel's team–mates at ADAC Berlin-Brandenburg e.V. He finished his debut season in eighth place with the highlight being a Pole position at Brno. He continued in the championship in 2005, switching to the Eifelland Racing team. He finished the season in 11th place despite missing three races during the year. Onidi also took part in the end–of–season Formula BMW World Final, held at the Bahrain International Circuit, but he retired from the event.
At the end of 2005, Onidi joined Fortec Motorsport to contest the British Formula Renault 2.0 Winter Series. He scored 20 points in the four races to finish 17th in the standings. He continued with the team into the main championship in 2006, finishing the season as the best rookie driver in 11th place. In 2007, Onidi joined the Motorsport Arena team to contest both the Eurocup Formula Renault 2.0 and Formula Renault 2.0 Northern European Cup. He took a best finish of eighth place to finish 20th in the Eurocup standings, whilst in the Northern European Cup, he took podium places at both Zandvoort and Nürburgring to finish ninth in the championship, despite missing the last six races of the season. In November 2007, Onidi took part in the four race Italian Formula Renault 2.0 Winter Series with RP Motorsport, taking two podiums to finish third in the standings. He finished level on points with the Cram Competition entry of Daniel Zampieri, but lost out on countback.
Euroseries 3000/Auto GP
For 2008, Onidi moved up to the Euroseries 3000 championship with the GP Racing team. He won his debut race at Vallelunga and took a second victory at Valencia later in the season to finish runner–up in the championship behind Nicolas Prost. In the accompanying Italian Formula 3000 series, he also ended the year as runner–up, finishing a single point behind Durango's Colombian driver Omar Leal. Onidi remained in the championship in 2009, moving to fellow Italian team Fisichella Motor Sport to partner Rodolfo González. He again took two victories during the season, at Portimão and Vallelunga, but despite leading the championship heading into the final round at Monza, he finished third in the standings, behind Marco Bonanomi and eventual champion Will Bratt. Onidi continued in the series for a third season in 2010, when the championship was re–branded as Auto GP. He raced for Team Lazarus in a single–car team. After taking a podium at the first event in Brno, Onidi added a further three podium positions to finish the season in eighth place, level on points with Carlos Iaconelli, who took seventh place due to his three race wins. He remained with Lazarus for the 2011 and was joined by compatriot Fabrizio Crestani; the two proved evenly matched, finishing fifth and sixth in the championship with Onidi seven points ahead.
