In case of diplomatic contact, the Tholians had designed a system that was specifically capable of being used by Federation translator technology which was only applied to their vessels on border patrols or on diplomatic duties. Encounter with any other kind of Tholian vessels meant the risk that they were unable to communicate with them as the Federation's ability to translate Tholian standard languages was limited in the 23rd century. (TOS novel: Constellations)
They have at least two kinds of written languages. One of which seems to be a cuneiform-like combination, with triangular marks combined into symbols.