Oastler grew up in Sydney with a keen interest in motorsport and earned a first-class honours degree in mechanical engineering from the University of Technology, New South Wales. He pursued a driving career in the early 1980s, achieving notable success in the Australian Formula Ford Championship. In 1985 he relocated to England to seek opportunities in European motorsport but found financial backing difficult to secure, and worked as a mechanic for Milldent Motorsport in Leicestershire in exchange for part-time drives in British Formula Ford 2000.
In 1986, Reynard recognised Oastler's engineering talent and hired him as a designer. He worked across several categories — Formula Ford, Formula Ford 2000, Formula 3000, and IndyCar — and his Formula 3000 chassis proved particularly dominant, going on to win five international titles. Oastler then led the IndyCar design programme from its inception; the resulting Reynard 95I won eight races in its debut season, claimed thirteen pole positions, and took victory at the Indianapolis 500.
In 1998, Oastler was seconded to the newly formed British American Racing team as chief designer, with responsibility for the design work on both the 1998 Tyrrell 026 (BAR having been built on the foundations of the Tyrrell outfit, which raced under the Tyrrell name in 1998) and the 1999 BAR 001. During the 1999 season he was promoted to technical director, though that role reverted to Reynard in 2000, returning Oastler to the chief designer position. When David Richards took over BAR management for 2002, Oastler departed the team.
Later in 2002, Oastler joined Jaguar Racing and contributed to the development of their R4 chassis. He was named Jaguar's chief engineer for 2003 and 2004. During Jaguar's turbulent final season in Formula One in 2004, Oastler decided to retire from professional motorsport. The team acknowledged his contribution before ceasing Formula One operations at the end of that year when Ford withdrew its backing.
Oastler returned to Australia, where he has been active in hillclimb competition, winning the Australian Hillclimb Championship five times. He has also shared engineering content through YouTube, continuing to engage with motorsport enthusiasts.
Oastler's contribution to Reynard's success in Formula 3000 and IndyCar placed him among the most prolific open-wheel designers of the mid-1990s. At a time when Reynard was disrupting established constructors in multiple series, his chassis designs delivered the competitive package that made the marque commercially viable. His Formula One career, while less decorated by results, brought that same engineering rigour to two teams navigating the sharp end of midfield competition.