Many of the societies you speak of were formed around several things.
What I think is the most common is the community you came >from in
Europe. For example, my maternal family came >from Kolomea/Kolomyja.
They were part of the Workmen's Circle, Kolomea Branch, and my
immigrant grandparents were buried there in NJ. That was for those
who were not ultraorthodox. As time went by, other groups became
popular like the Knights of Pythias. They were not really a Jewish
group. Membership was just based on "belief in a Supreme Being" or
monotheism. But they had cemetery plots around the country.
I would recommend as a starting point, the location of the burial of
your relatives. Jewish cemeteries are often marked off by the
fraternal organization which sold the plot to its member. If your
family was poor, they might have been buried by the Hebrew Free
Brooklyn, New York