Oviedo played his entire club career in the Argentine league system, starting with Instituto de Córdoba in 1973.
In 1974 he was signed by Instituto's fierce local rivals Talleres de Córdoba. Over the next eight years Talleres were one of the strongest teams in Argentina, they reached several Semi-Finals in the Nacional championships and lost the final in 1977 on the away goals rule to Club Atlético Independiente.
In 1983 Oviedo joined Independiente, helping the team to win the Metropolitano 1983 championship in his first season with the club and the Copa Libertadores in his second season.
In 1986 Oviedo returned to Talleres but after one season in Córdoba he moved back to Buenos Aires to play for Deportivo Armenio he stayed with the club between 1987 and 1992 despite their relegation from the Primera in 1989.