Oswald was born and raised in St. Vital, Manitoba, and was a teacher and school administrator for fifteen years before entering politics. She initially taught English, later serving as vice-principal at a special-needs school in the Louis Riel Division. In the latter capacity, she frequently worked with children and families who arrived in Canada from war-ravaged countries. Oswald has also been involved in local groups such as the Victoria Hospital, the Zoological Society of Manitoba and Take Pride Winnipeg!.
Oswald was part of the NDP's historic breakthrough in south-end Winnipeg in the provincial election of 2003, defeating incumbent Progressive ConservativeLouise Dacquay in the riding of Seine River, 4,314 votes to 3,582. The NDP had never won this riding before. Oswald's campaign focused on greater access to post-secondary education and a tuition freeze for university students.
In August 2004, Oswald was appointed to lead a task-force committee looking for ways to encourage physical activity in the province's youth.