So you have ascertained his given name? What is it?

If you have his mother's maiden name, I can try running a search for both surnames simultaneously thru Ukrainian internet. I have had some success doing that.
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Russian Consular Records available thru NARA:
http://www.archives.gov/research/guide-fed-records/groups/26...
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New Russia Township > Lorain County > OH. Orthodox Churches???

Grandfather came w/a special kind of spirituality. Being so far away from home, he would have been a parishioner of one of the three Ukrainian Orthodox Churches in Lorain. He would have married there and had his children baptized there. Orthodox church records are full of detail like name of parents, and their parents, and where they lived and what they did for a living.

Start w/inquiry at St. Mary's Ukrainian Orthodox Church in Lorain, OH. This originated as a Carpatho-Rusyn Church, but you never know.
http://www.stnicholaslakewood.org/StMarys/index.html
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PS > July 8, 1896 DOB - stay flexible w/month and day, because this date may be his baptismal date or his actual birth date. In Grandfather's time frame in what is Ukraine today, baptismal dates were considered birth dates. Children were frequently born at home and the child would be baptized within 10 days of birth. To this day the birthday in Ukraine is not as important as the Name's Day is.