The Eastern Orthodox Church of Antioch (based in Damacus and having jurisdiction over most Orthodox Christians in the Middle East) currently uses Arabic as a liturgical language.

EDIT: Along the Silk Road in Central Asia, Persian would have been the primary lingua franca, even after the Arab conquests.

The liturgical language of the Buddhism spread across the silk road was Sanskrit. The Tang dynasty monk Xuanzang wrote in his account that he was able to communicate with the nobility and priests living in the various Buddhist kingdoms along the route to India in Sanskrit. The Central Asian priests who were most influential in transferring Buddhist teachings from India to China generally spoke Iranian languages like Bactrian, Sogdian, and Tocharian.

Alhough I don't know of any Dharmic religious movements that used Arabic as the liturgical language, the Druze are a religious group in (particularly) Lebanon, Israel, and Syria. It is often thought that the Druze are Muslims or Christians, and many associate themselves as one or the other, or even as their own religion, so it is difficult for me to say that they are their own religion.

When the Ottoman Empire collapsed after WWI, the city of Antioch ended up within the borders of the new state of Turkey. The Patriarchate moved its headquarters to Damascus to avoid persecution from the Turkish government. Up until recently the Syrian government had protected the Christian minorities within Syria, but now with the civil wars of the "Arab Spring" bringing chaos and destruction and giving a free hand to radical Islamist groups, that relative safety is gone.