Oniskey was a two-way tackle as a junior and senior and was a regular defensive guard as a sophomore. He started every game during his three-year varsity football career. Oniskey received numerous accolades following his senior year, including Associated Press All-America honorable mention, AP All-Ivy first team, AP All-East second team, United Press All-East honorable mention, and All-Catholic All-America, in addition to being selected to several all-opponent teams. He was a second-team AP All-Ivy pick and received AP All-East honorable mention in 1953, when Cornell won the unofficial outright Ivy League title. The Big Red tied for the Ivy championship in 1954, when Oniskey was voted co-team MVP. He was a seventh-round draft choice of the Washington Redskins, for whom he played until he was traded to the New York Giants. He won the University heavyweight boxing championship in 1955.
