Your surname is ???????? in Ukrainian.It transliterates as (sounds like) Slobodyan/Slobodzan + all the other transliteration variants you have encountered in your research.This is a very old Eastern Slavic name, which means ONE WHO LIVES IN A SLOBODA.Sloboda was a kind of colonization-type settlement in sparsely populated lands in Eastern Slavic history (in what is Ukraine, Belarus and Russia proper today). The place name is derivedfrom a very early Eastern Slavic word for FREEDOM.Initially the settlers of such slobodas were freed from various taxes and levies. Freedom from taxes was the incentive for colonization. By the first half of the 18th century this privilege was abolished, and slobodas became ordinary villages, some still retain the place name, Sloboda.
Today there are appx 14,000 residents w/this surname in Ukraine. Locating the exact place of birth for your Immigrant Ancestor is key to moving your research across the Atlantic.
Mathew D. Slobodianwas born in 1935.It is very unusal for Ruthenians/Russniaks/Ukrainians to have a middle name.Chances are Matwij (Mathew in Ukr) was using a patronymic and his father's name might have been Dmytro or Danylo??? ------------------------------------------------------------
Both Zlateca and Jerry are very knowledgeable genealogists.Take their advice.
Zlateca has provided you with some exc clues.What religion did your family practice?Look for the nearest Ukrainian Church in PA and request a metryka (Baptismal Certificate).There you should find loads of info, including place of origin for parents.
I do agree w/Jerry, that it is highly probable that your Immigrant Ancestors were not SCHLACHTA (nobility). Certainly that has very little to do with who you are.You have much to be proud of, especially if your origins are serf or peasant. Your Immigrant Ancestor, traveled halfway around the world, in what was technically a cargo hole, in the hope that he could provide a better life for his family and himself.That took unusual courage for someone, who verylikely had never been more than 30 miles from his place of birth, before this very long trip to a strange land, strange language and strange culture.