Elia is one of the few Ohio State players in the modern era to start on both the offensive and defensive teams. He graduated from Cliffside Park High School in New Jersey in 1971, where he had played as both a running back and linebacker. He was recruited to Ohio State by head coach Woody Hayes as a fullback. Before the third game of the 1972 season, Elia was claimed by the Ohio State defensive coordinator, and made into a linebacker.
Early in the 1973 season starting fullback Champ Henson was injured, and freshman backup Pete Johnson was judged unready to take over. Hayes moved Elia back to the offense as fullback. That season Elia led the Buckeyes in scoring (14 touchdowns for 84 points). In 1974 he returned to linebacker and was the team's leading tackler (144 - 74 solo, 70 assisted).
Elia was selected in the fourth round of the 1975 draft by the Miami Dolphins as a linebacker. Prior to the 1976 season he was taken by the Tampa Bay Buccaneers in the expansion draft. Tampa then traded Elia, wide receiver Willie McGee and a second-round draft pick to the San Francisco 49ers for quarterback Steve Spurrier. Elia spent the next three years with the 49ers.