I have been in touch with a woman in Buenos Aires whose maiden name is Steinberg. She found me through a Facebook post in a group called Who is a Steinberg?.
I have recently discovered that my Steinberg great-grandfather (alternately identified as Chaim Moshe Steinberg, Moses Steinberg or Moritz Steinberg) left Odessa with his father at the time of the pogrom in 1859. They went to Bucharest. I have had a very difficult time finding any concrete information about the family. He married Malca (Maria) Askenasy in Bucharest and eventually moved to Berlin. In the late 1930s he left Berlin for Palestine, accompanied by one of his daughters and her family (husband and son).
If anyone has more information on this family thread I'd be most interested.