Too young to qualify for the 1988 Olympics, she made her senior debut in 1989 and represented Hungary at the World Championships that year, where she placed 19th in the all-around and 5th in the balance beam event finals.

At the 1991 World Championships Ónodi suffered a sudden back injury, but was able to win a silver medal on vault and helped the Hungarian squad qualify for the 1992 Olympics with an eighth-place finish in the team final.

She tied with Romanian Lavinia Miloșovici for the gold in the vault event final; on floor exercise, performing to "Hungarian Rhapsody" she finished second behind Miloşovici.

Ónodi's difficulty level on vault was actually higher than Miloșovici's (they both used full twisting Yurchenkos but Henrietta did a piked barani and Milosovici a tucked).

[3][4] In 2001 Ónodi graduated with a degree in marketing and found a job in Miami, Florida, as Director of Community Relations for the World Olympians Association.