The HalGal Database:

Search the Greek Catholic church registers held at the Central State Historical Archives of Ukraine, city of Lviv (TsDIAL).

Viewed in Polish and Ukrainian Transliterated Forms.

Fortunately, the massive collection of Greek Catholic parish vital record books are available on microfilm through the Family History Library.  And even better, the parishes and villages have been cataloged!

Visit www.FamilySearch.org.  Then click on "Search", and select "Catalog".  You can then enter your parish and/or village name to see if a microfilm exists.   

Please note that vital records were kept at the parish (for Jewish records, they were kept by the local Jewish congregation).  Therefore, it's critical for you to know the parish/congregation.  However, the FHL catalogers have done a good job noting many of the villages involved, so it's a good idea to check BOTH your ancestral village/town and ancestral parish/congregation.