O'Reilly was born in Isleworth, now part of Greater London. He played for Grays Athletic before turning professional with Tottenham Hotspur in 1979, and made his debut the following year. After 45 League games for the club, he joined Brighton &amp; Hove Albion for a £45,000 fee. He stayed with Brighton for two-and-a-half seasons before moving on to Crystal Palace. He scored in the 1989–90 FA Cup semi-final as Palace beat Liverpool 4–3 after extra time, and then scored the opening goal in the final, against Manchester United. The match ended in a 3–3 draw, and Palace lost replay 1–0 five days later.