Vaskó started to play football in smaller clubs and joined Vasas in 1998. Three years later he started to play for Újpest Football Club, and he has been with the team ever since, except for a year he spent on loan with Football Club Tatabánya. In 2006, despite his young age, he became the captain of Újpest Football Club. Vaskó was on trial at Southampton F.C. during July 2007, but he failed to make sufficient impression and was not signed by the Championship club
Vaskó has now sealed a year-long loan deal with newly promoted League 1 runners up Bristol City.
At the end of the loan deal Bristol City have the option of signing the defender on a 3-year contract. However, he was sent back to Újpest Football Club after Bristol City did not wish to sign him permanently.
Now is a player of United States Avellino Italy second division. However, his spell at Bristol City seems to have made a lasting Impression on the clubs management, who have been rumoured to have made a bid to resign the Centre Half permanently.
But instead he moved to Italian side Avellino.
His loan spell ended after the 2009 season and he returned to Újpest Football Club.
His nickname whilst at Újpest Football Club was "The White Rhino" because of his immense size.