Strasburger attended Holdrege High School, where he was a starter at defensive end and was named All-state as a senior.
As a true sophomore, he was a backup right defensive end behind All-Big Eight selection Tony Felici.
His most famous play came in the eleventh game against Oklahoma University, intercepting a pass late in the fourth quarter that he returned 22 yards to the opponent's one yard in the final 30 seconds of the game, helping the team clinch a 28–24 victory and win the Big Eight Conference Championship.
As a senior, he made 12 tackles for loss (tied team lead), 7 pass breakups (school record for linemen).
[4] Strasburger was selected by the Dallas Cowboys in the ninth round (243rd overall) of the 1985 NFL draft, to play him at outside linebacker.