The marriage record for Sadie gives her place of birth as Zaga, Russia
The NY arrival record, 14 July, 1899 aboard the Pennsylvania as Sore Solberg says Zagarny
The Hamburg departure  record , 2 July, 1899 aboard the Pennsylvania says  Zagarny
She is traveling with other family members, including  brother Nachum.
Jewishgen's Memorial Plaque Database has a plaque for Nattan Solberg,  Nachum  son of Eliahu Shimon.  The plaque, is in Somerville, MA.

There is a Zhagar in Lithuania.  https://kehilalinks.jewishgen.org/zagare/community.html           
Jewishgen's Lithuania Database     https://www.jewishgen.org/databases/Lithuania/    has a number of records for variations on the Solberg name, but  I could not find any for Eliahu Shimon.  Also a number of records for variations for Bick. There is a Sheine.

David Rosen
Boston, MA

Zaga/Zagarny are definitely referring to Zagare in far northern Lithuania. My Lak/Lock family hails from this town.

The reason you are having difficulty finding records is because the Russian empire birth/marriage/death records for Zagare and most other towns in the Siauliai district were lost, sometime around World War I. It does make it more challenging to find evidence for our forebears because of this.

However, there still are tax lists, some revision lists, and a few other records for the town.

I also found records for related Lak individuals living in Riga, Latvia, where many folks from the far north of Lithiania re-located to, starting in the late 1800s. 

For your searching, use the 'Sounds like' function for the surnames, since they can be spelled so many different ways.

--
Michele Lock

Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Rabinowitz in Papile, Lithuania and Riga, Latvia
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus

Thank you for your reply, David (and others). It is all very much appreciated as I continue searching.

I have established a tremendous amount of information about Sadie (my great-grandmother) and her siblings once they came to Boston, Medford and Somerville). They originally all lived with their oldest brother Lyon Philoph Solberg (and were incorrectly noted on the 1900 census as his children). All 8 children came to Boston without their parents Simon Solberg and Jennie Bick, and my grandmother says Sadie came here as"an orphan." All of this indicates that Simon and Jennie were already deceased by 1899 when their children emigrated to the US. 

I am going to continue searching using the different possible spellings and regions they could have lived. Thank you for all of your input and help. My fear of course is as Michelle stated, that the records are simply lost forever. 

Warmly, 
Eliza Wheeler