Over the next few years, Ónodi established herself as a medal contender at major events. In 1989 she became the first female Hungarian gymnast to medal at the European Championships with a gold on the uneven bars; at the 1990 Europeans she placed third in the all-around and the floor exercise. In 1990, she also finished third in the all-around at the Goodwill Games and the World Cup where she won the vault event. 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.