Oakar, who graduated with a B.A. from Ursuline College in 1962 and an M.A. from John Carroll University in 1966, taught at Lourdes Academy, a Catholic high school for women, directed plays, taught at Cuyahoga Community College from 1968 to 1975 and served on the Cleveland City Council from 1973 to 1976 before winning election to the House from Ohio's 20th congressional district in Cleveland's West Side and the surrounding suburbs. She took office in 1977, succeeding James V. Stanton.
Oakar, one of only a handful of Arab-American members of the House, became regarded as an increasingly powerful member of the House. She was a high ranking member of the Banking, Housing and Urban Affairs Committee, the Committee on Post Office and Civil Service and the House Administration Committee. Oakar's high placement on these committees allowed her to bring home to Cleveland large sums of money for urban renewal. Oakar forged strong relationships with Jewish groups in Cleveland. In the late 1980s, Oakar was elected the Secretary of the House Democratic Caucus.
In 1991, she was one of nearly one-hundred Members of Congress in a widespread House Bank controversy involving overdrafts, even though the House Bank was not a financial institution per se.
In 1992, her district was renumbered the 10th and redrawn to include more Republicans, though it was still heavily Democratic. Oakar withstood a challenge from Tim Hagan in the Democratic primary — Hagan had been endorsed by Cleveland Mayor Michael R. White — but lost to Martin Hoke in the general election.
Oakar pled guilty to violating campaign finance laws, a misdemeanor in the early 1990s.
She won a 1999 libel settlement against Cleveland's newspaper, The Plain Dealer.
Oakar unsuccessfully ran in the 2001 Cleveland Mayoral Primary and served a single term in the Ohio House of Representatives from 2000 to 2002.
Currently, Oakar is president of the American-Arab Anti-Discrimination Committee (ADC), which describes itself as the largest Arab-American grassroots civil-rights organization in the U.S.