A few minutes ago, I posted a response on this board about a Roman Catholic directory of national scope that was published in 1922. It lists St. Mary's Orphan Asylum, 56 Ball St., Port Jervis, which is in Orange County, NY. Conducted by Sisters of Charity of St. Vincent de Paul.
One can also check the annual editions of the "Official Catholic Directory," published by P.J. Kenedy. It contains locations of the motherhouses of the orders of nuns, priests and brothers. As well as the names of Catholic schools and institutions and parishes.
A 1977 directory lists Catholic Charities, 30 North St., Middletown, NY---then under the supervision of the branch in New City [not New York City], but part of the Archdiocese of New York, which is based in Manhattan, a borough of New York City, as you know.
I haven't answered your question about the disposition of the Asylum's records because I don't know. One can ask the Archdiocese before tracking the order of nuns. There are also some censuses which may list the children, the federal census of 1920 (indexed by name under the Soundex system) and the 1915 and 1925 New York State census, which are not indexed by name as far as I know.