Nate was signed by the Los Angeles Dodgers in 1959.  

He came up to the majors for the first time in 1963, a year the Dodgers won the World Series. He appeared in 65 games, playing primarily second base. 

The next year, in 1964 at age 23, Nate had his most at-bats in the major leagues

In the off-season, he was traded to the San Francisco Giants in the deal involving Ron Hunt and Tom Haller. 

In the off-season before 1969, he was traded to the Yankees, and played one game with them before they traded him to the Cubs, where he finished out his career.

Played amongst infielders Ernie Banks, Ron Santo, and Don Kessinger.

In 1989, Oliver managed the Arizona League Angels, and in 1990-91 he was at the helm of the Palm Springs Angels.

In 1998, Oliver managed the Arizona League Cubs and in 1999 managed the Daytona Cubs, and in 2000 was a roving infield instructor in the Cubs organization.

In 2003, he took over the managerial reins of the Saskatoon Legends of the Canadian Baseball League in mid-season from Ron LeFlore.

In 2006, Nate was the bunting instructor for the Chicago White Sox organization.