For his performance, he was nominated for a Young Artist Award and a Saturn Award. In 1990, Oliveri starred as Danny Flocken in the pilot of The Flockens, a show about raising four boys, which also starred Miriam Flynn and Bruce McGill as the parents. The show was not picked up and dismissed. He starred in an episode of Monsters and then landed the role of Kevin in Edward Scissorhands with Johnny Depp and Winona Ryder.
He later starred in an episode of ABC Weekend Special as Ryan in Ralph S. Mouse. The next year, Oliveri reprised his role as Nick Szalinski in 1992's Honey, I Blew Up the Kid. His character had matured since the previous film and took a liking to Mandy Park, which was Keri Russell's film debut. Oliveri was asked to reprise his role as Szalinski again two years later for the 3D science fiction film, Honey, I Shrunk the Audience, that opened at Epcot in 1994 and closed in 2010. It was later added to Disneyland's Tomorrowland section in California, but it closed in 2010 there, too.
At age nine, Oliveri starred as Paul Bard in an episode of ABC Afterschool Special. Two years later he made a guest appearance on Friday the 13th: The Series, based on the film franchise, as Mike Carlson. That same year, he starred as Young Nelson in the television movie, Ask Me Again. Also that year, he landed the role of Nick Szalinski, the son of Rick Moranis's character in Honey, I Shrunk the Kids.
