Oyama began performing stand-up comedy at 17 years old. In 2012, she was a state finalist in the Class Clowns competition. That year she also performed at The Sydney Fringe as part of "Barely Legal - Australia's Best Young Comedians" alongside Neel Kolhatkar and Aaron Chen, and performed on Dan Ilic's FBi Radio show. Oyama became a writer for the children's sketch comedy show You're Skitting Me, and made her television debut performing stand-up comedy on SBS 2 in 2014.

In 2017, Oyama was cast as executive assistant/receptionist Courtney Kano in the third, fourth, and fifth seasons of Utopia. In the same year, she joined the cast of ABC Comedy's topical entertainment show Tonightly with Tom Ballard as a writer; she also starred in the second and final series of the show in 2018.

Oyama directed, co-wrote, and co-starred in The Angus Project, a web series and television pilot that aired on ABC iview in 2018. Based on real events in Bathurst, the series co-stars Angus Thompson as a sports journalist with cerebral palsy, for whom Oyama becomes a friend and caregiver. The show received praise for its earnest depictions of disability and regional Australia.

As of 2019 Oyama was regularly performing stand-up comedy.

In 2020, she starred on the Network 10 sketch comedy series Kinne Tonight, and served as a scriptwriter for Michael Cusack's Adult Swim series YOLO: Crystal Fantasy. She co-directed the film Diving In, which starred an amputee swimmer and was featured in the 2020 Sydney Film Festival. Also in that year, Oyama received media attention for making "#CatPoop" a trending topic on Twitter in Australia.

On 9 July 2024, Deadloch was renewed for a second season and it was announced that Oyama would reprise the role of Abby Matsuda. On 28 October, Oyama was named for the animated film The Pout Pout Fish.

On 4 June 2025, Oyama was announced as part of the cast for the series Gnomes.