He started playing violin at an early age being first taught by his stepfather, a renowned local wedding toast-master and fiddler, and later by M. Chait in Karl Lagler's Music School.
After working in city's theatre orchestras for several years, he was accepted into a newly founded Odessa Conservatoire where he studied composition under Witold Maliszewski.
Shteynberg composed music to more than 150 plays, including “Tevye the Milkman”, “Wandering Stars”, ”Stempenyu” by Shalom Aleichem,”Favourful people” after Mendele Mocher Sforim, ”Uprising in Ghetto” by Peretz Markish, ”In fire” by M.Daniel, ”Russian People” by Konstantin Simonov, ”The Merchant of Venice”, “The Taming of the Shrew ” by William Shakespeare etc.
Shteynberg was also a prolific writer of symphonic and chamber music, songs, and arrangements of ethnic tunes by peoples of Jewish, Ukrainian, Kazakh, Uzbek and other origins.
His music, rooted into a late-romantic tradition of the turn of the 20th century as well as Jewish cantorial and klezmer heritage, was recognized for its beauty, expressivity, compositional depth and sophistication.