If your Rechnitzer ancestors lived in Vienna between about 1895 and 1925, you have a promising source in form of the Vienna residency records as filmed by LDS. Send me an e-mail with more details and I'll try to give you more specific advice.
There are other sources available from LDS for Vienna like male birth records, Jewish records, and cemetery records, but it would be best to first get a handle on the addresses (and districts) where your ancestors lived.
Réte was in old Pozsony (Pressburg) county, now in the Slovak Republic. The population was mostly Magyar, but there were strong Czech and Jewish minorities which would fit with the names in your posting, respectively.