[1] Oliver and the Fishermen won the Manitoba Senior Hockey League in 1919 and challenged the Hamilton Tigers for the Allan Cup.

Oliver quickly established himself as a star player in the WCHL,[3] using his speed and shot to earn positions as a First-Team All-Star in both 1924 and 1925.

[4] He was a key member of the Tigers' team that won the 1923–24 WCHL championship,[5] and lost to the Montreal Canadiens for the Stanley Cup.

His NHL career began on a line with Bill Carson and Percy Galbraith, and he led the Bruins in scoring each of his first three seasons with the team.

[4] Oliver became the first Boston Bruin to score a playoff overtime goal when he notched the winner on March 20, 1930 versus the Montreal Maroons.