Strelnikov was born in 1939 in Odessa, Ukrainian SSR, and made his studies at the local art academy. He is a member of the Odessa Group of exiled and dissident artists. In 1960, he debuted in Odessa at the autumn exhibition of the Fine Art Federation and took part in several officially-approved exhibitions in the Soviet Union and abroad until 1971. His art career resulted in loss of official approval, and from 1972 he was forced to relegate exhibition to private households in Kiev, Odessa, Moscow and Leningrad (now Saint Petersburg).
In 1978, he emigrated from the USSR to Vienna, Austria. The following year, he settled in Munich, Germany, where he has worked and lived since.