Barcelona advanced into the last four 6-1 on aggregate after winning the first leg 1-0 in Italy.
Before the second-leg tie against Roma, Oshoala had erred to score in her last four matches for Barcelona.
Oshoala set up teammate Fridolina Rolfo for the first goal in the 11th minute.
The Super Falcons striker made it 4-0 just one minute into the second half.
Barcelona will encounter either Chelsea or Olympique Lyon in the semi-finals in April.
