Hope you are still around and reading posts . . . but I don't see any reason to suspect it is a Russian name.From more knowledge people than I am, who post on a forum at It's All Relative, I learned that the -sky on Slovak names can mark it as a place name rather than a patronimic of some sort.So, that would seem to indicate that the first of our "Olsavskys" was someone from "Olsav".In the general area, there is an "Olsov" (this is between the Nova Lubovna someone else here mentioned and Presov [my Olsavskys are from Vitaz, just west of Presov]).There is also an "Olsavce" just north and slightly east of Presov.
My Olsavskys were Lutheran.I seem to recall reading somewhere about some Olsavskys who were Eastern Rites Catholics.