Varadi went on to become a nomadic journeyman, who rarely spent more than two years with any club and never made 100 league appearances in the colours of any team he played for.
He was part of the Leeds United side that won the old First Division in 1992 but only played in three matches which was not enough games to earn a winner's medal. He was also part of the Sheffield Wednesday side that won promotion to the First Division in 1984, after 14 years away. He was sold to West Bromwich Albion a year later and was their top scorer with nine league goals in 1985–86, but was unable to prevent them from being relegated in bottom place with just four wins in the league. He was then sold to Manchester City, and was unable to prevent their relegation the following season, although he did help them reach the quarter-finals of the FA Cup in his second campaign there. He was nicknamed "Imre Banana" by the City fans, following the inflatable banana craze which the club's fans helped start that season. He scored 26 league goals in two seasons at Maine Road.
He left Maine Road to sign for Sheffield Wednesday for a second time in the summer of 1988, and spent two seasons there, but after 18 months he was sold to their Yorkshire rivals Leeds United in February 1990. He spent three years at Elland Road, helping them win promotion to the First Division on his arrival, but rarely played for Leeds in the First Division due to the arrival of new players in the midfield and forward positions. He did not make enough appearances in 1991–92 to earn a league title medal. He had loan spells at Luton Town and Oxford United before finally exiting Elland Road and dropping down two divisions to sign for Rotherham United in the summer of 1993.
He spent two seasons at Millmoor, scoring 25 Division Two goals, before brief spells at Mansfield Town and Scunthorpe United. He called time on his professional career in 1995 when he became player-manager of non-league Matlock Town, before joining Guiseley.[6]