There is quite a variance, actually.
The African Oriental Orthodox are on the general old rendering like the Russians: they celebrate Pascha with the rest of the Orthodox and the Nativity of Christ on January 7th.
The Asian Oriental Orthodox are different. The Syrians generally use the equivalent of the Revised Julian Calendar (with the exception of the Diocese of Jerusalem), celebrating Pascha with the rest of the Orthodox, while celebrating the Nativity on December 25th. The Indians, however, generally both use the equivalent of the Gregorian calendar, celebrating both Pascha and the Nativity with the West. The Armenians are yet also different. They generally use the rendering of the Gregorian calendar (again, with the exception of the Diocese of Jerusalem), however, they have no detached the celebration of the Nativity from that of Theophany (being on January 6th for most Armenians places; January 19th in Jerusalem).