Question: Do we know anything at all about Tolkien's Avarin languages; what they would sound like, how they'd name themselves etc? We read quite a bit of Sindarin and Quenya words, but I can't seem to recall a single mention of what tongue the Avari would speak?
Answer: I’m no Stephen Colbert or askmiddlearth but to give my thoughts on this I’d like to start with the fact that the Avari themselves as elves are the least talked about or mentioned in all of Tolkien’s Legendarium. Which is quite a bit of shame since I find them absolutely fascinating.
In canon we are told that the Avari live far and wide throughout Arda and from my immediate memory I remember mentions of them living in the forests south of Harad, from where the Mumakil come, in the far east where the Orocarni mountains are, in Taur Romen and to the north of the Forochel Bay. But the last two are demi-canon since they come from MERP. Also in Nan Elmoth during the First Age. But that’s a separate case altogether since Beleriand is long under the sea by the Third Age.
Since Prof. Tolkien was fond of comparing Middle-earth to an early version of our own world and many of the people of Middle Earth have attributes similar to real life cultures - such as the Rohirrim being Scandinavian and using runes in writing, the Dunlending being Celts, the Easterlings being Mongolian, the Hobbits living in a society mirroring 18th century England and so on. Based on the geographic locations of the Orocarni I would not rule out Avarin, or at least some dialects of it to be a Middle-earth equivalent of Arabic or Hindi. To my shame I am not familiar with the many languages spoken in Central or South Africa, so I cannot give my thoughts on how well it would translate to Harad Avarin. Wikipedia tells us that there are three branches of Avari, so I would definitely not rule out a more varied net of languages than can be used.
As a final note, Parf Edhellen an excellent dictionary for Tolkien languages gives us small clues for how Avarin may sound like or at least where it started from. I searched the word “night” and from all the results the closest I imagine Avari elves would use is the Primitive Elvish “dōmē“.