Thanks to help from suanj, I've cracked my father's mother's side of the family. My father's father is another story. While my grandmother's family was from Marianapoli in Sicily, my grandfather's family was from Postiglione in Salerno province outside of Naples. My grandfather Giuseppe Vecchio was born in Postiglione in 1891 and came to the US in 1910. He became a US citizen in 1916 (according to an early census). He had several brothers - Biagio, Lorenzo, Vincenzo and Leo (I think). On his Immigration I think it said he had a sister back in Postiglione, but it's hard to read the name. I also "think" his father was named Giovanni and his mother Maria. I can't find anything on them yet, because I don't believe they ever came to the US, and there are no records online (that I've found) for Postiglione where I can check birth or marriage records. Some of this kind information is available on FamilySearch.org for some Italian towns, but not for this city. I think I read somewhere this may be in progress, but I'm pretty much stuck unless I go visit the town and go to the place that keeps the records and spend some time searching them. Or even search the cemeteries. But I think Vecchio was a pretty common name in this town, so there are LOTS of them!
Anybody know where I might find records for Postiglione? Or am I correct and they are NOT online yet.