Ovadia was born in Plovdiv, Bulgaria in 1946 to a Jewish family who moved to Milan in Ovadia's early childhood. Here he graduated in Political science, and debuted in the theatre world under Roberto Leydi, as singer and musician in the band Almanacco Popolare. In 1972 he founded a company, the Gruppo Folk Internazionale, playing mainly songs and music from the Balkans.

Ovadia debuted as theatrical actor in 1984. In 1990 he created the Theatre Orchestra and produced Oylem Goylem, which he successfully toured in Italy, France, Germany and USA. Oylem Goylem (Yiddish for "The world is dumb") skillfully melted satire and klezmer music sung by Ovadia himself. In 2005 the spectacle was broadcast by RAI, Italy state TV.

In 1995 Ovadia wrote Dybbuk, about the Shoah, considered one of the most important Italian theatrical show of the period. In the same year he produced Taibele e il suo demone and Diario ironico dall'esilio, written with Roberto Andò. His following spectacles include Ballata di fine millennio (1996), Pallida madre, tenera sorella (1996), Il caso Kafka ("The Kafka File", 1997, with Andò), Trieste, ebrei e dintorni (1998), Mame, mamele, mamma, mamà... (1998), Joss Rakover si rivolge a Dio (1999), il banchiere errante (2001), L'armata a cavallo (2003).

In 2005 he collaborated with band Modena City Ramblers for their album Appunti partigiani.He has been an outspoken opponent of what he regards as growing racism in Italian society. He received an award from the University of Pavia in October 2007; in his acceptance speech he denounced the treatment of immigrants, especially Roma.

In Sept./Oct. 2003 Mr. Ovadia gave an extensive interview to Vered Zaykovsky of the Israeli cultural magazine "Eretz Acheret". It can be found at www.jewish-theatre.com.