Born in New York City, Oster was listed as 6 feet 3 inches (1.91 m) tall and 198 pounds (90 kg).

Oster was signed by the Athletics as an amateur free agent on August 20, 1954, and made his MLB debut three days later.

[1] His only decision came a little over a month later in his final MLB game when the Athletics were defeated by the New York Yankees, 10–2.

He allowed one earned run, three hits and five bases on balls in three innings of work before exiting for a pinch hitter, trailing 4–1.

[1] In his eight career MLB appearances, he worked in 152⁄3 innings and allowed 19 hits, 12 bases in balls, and 15 runs, 11 of them earned.