My father, Kostos Constantine Kalagias, was from the island of Chios where all of his family originated from.
I am not sure if Kalogreas is another form of the name, but I do know that Kalagias was and continues to be how it is spelled on Chios.
My father was previously married (before he married my mother)to a woman whose family was Pappis (their choice of spelling the name when they arrived in the USA).
My dad arrived in the USA after jumping ship in the early 1930's. He lived in Westchester, NY and then the Bronx, NY. One of his brothers, Macadia Kalagias, came to the US and lived in Queens,NY as did one of their sisters,Helen Kalagias-Apostolidis. A second sister,Marika Kalagias-Lamanis, settled in Springfield Mass with her husband and family.
We have been in contact with other Kalagias' in the USA, and although they use the same spelling, they pronounce the name differently, and claim no relationship to the Chios clan.
I'm sorry I couldn't be of more help to you. Try doing a Kalogreas search on several of the internet telephone white pages. Maybe you'll come up with some names and address of people that you can contact by letter to see if they are family, or at least they may be able to provide you with some leads.