Harry was the 1960 OHSAA state champion at the 154-pound division in wrestling.

After graduating from Parma Senior, he wrestled at Ohio University where he compiled a 76-3 record. While at O.U., he won 4 Mid-American Conference championships and was a two-time NCAA All-American, placing second in the nation in 1963 and winning the national championship in 1964. After college, Harry was a member of the Olympic team, taking fourth at the FILA World Championships. He was an alternate on the 1964 U.S. Olympic team and won a gold medal at the Pan-American games in 1966.

He placed fourth at the World Wrestling Championships in New Delhi, India. After his wrestling career ended, Harry became the Head Coach at Ohio University, where he won 11 M.A.C. titles and earned M.A.C. coach of the year five times. He is a member of the Ohio University Hall of Fame, Ohio and the National Wrestling Hall of Fames.   

Houska is a charter member of the Parma Senior High School Athletic Hall of Fame, inducted in 2007.