Engonga came from a football family. His father Vicente was also a footballer who left Equatorial Guinea in 1958 and settled in Torrelavega, playing for Gimnástica de Torrelavega and other teams in the region. Óscar was the youngest of four brothers (all former players), the most prominent being older Vicente, who represented Spain at UEFA Euro 2000; Óscar and Vicente coincided at Gimnástica – with siblings Julio and Rafael – and Valladolid in the 1991–92 season.