As far as I know, the only Vadeanu family in Binis is the one that I belong to. Therefore, since your father was born there, we must be related.
The story of the Vadeanu's in Binis, as I know it, starts with a priest, Popa Vadeanu (Ioan Vadeanu I think was his name). He got posted there in the 30's or 40's. His nephew, also Ioan Vadeanu (my grandfather), came to visit him, met Elena Iova (my grandmother) a local from Binis, married her, and stayed there. After this, a further nephew and niece of Popa Vadeanu did the same - Dinu Vadeanu and Lucretia Vadeanu.
There is a further Vadeanu branch in the area, that we are in contact with. An uncle of my grandfather (which could have been a brother of Popa Vadeanu) married a Serbian woman in a nearby town (a Serbian town in Romania), so this Vadeanu branch in Banat is mainly ethnic Serbian.
I am the son of Ioan Vadeanu's (the nephew, not Popa Vadeanu) daughter, Emilia. We are in Melbourne, Australia. My mother also has a brother, Mircea Vadeanu, who lives somewhere in Africa, Liberia I think. Two of his children, my cousins, live here in Australia, and one of his daughters is in Binis, Romania. She is the last Vadeanu, besides my ageing grandfather there.
Radu, are you a descendant of Popa Vadeanu? I thought he only had two daughters, and, as far as I know, they both emigrated to the USA after WW2.