At the 1987 World Championships in Rome, she won a bronze medal in the 100 metres hurdles with a time of 12.46s as well as silver medal as a member of the East German 4 × 100 metres relay team.
She also won the 1987 World Indoor 60 m hurdles title, two World Cup 100 m hurdles titles and three European Indoor 60 m hurdles titles.
Her world indoor record for the 50 metres hurdles of 6.58 secs in 1988, still stands (as of 2019).
Oschkenat won eleven East German individual national titles, taking five titles in the 100 m hurdles between 1984 and 1989 at the East German Athletics Championships, as well as six consecutive titles in the 60 m hurdles at the East German Indoor Athletics Championships over that period.
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