After Alexander's conquests they seem to have been heavily hellenized.
The other fascinating thing to me about that area is the Hurrian peoples - were they ancestors to the Kartveli people? Were they relatives to Sumerians, Elamites and Dravidians (all sharing an agglutinative language)
They seem to have been happy with their pantheon.
Most of the various Anatolian languages were related, that seems to have carried over to the island culture known as Minoan. Herodotus probably spoke and/or understood Carian, since he grew up in a town with a Carian minority, and his closer temporal proximity gives his opinion weight. Etruscan (another related language) turned Apollo (himself a non-Greek deity that was adopted by the Greeks to the degree that he became the quintessential Greek deity) into something like Up-pu-lu. The Hurrians were the Carians.
The Ionian Greeks settled in the Anatolian underbelly as colonists, a late coat of paint as it were, and the Lydian kingdom, while it lasted, kept them out of Persian domination. Once Persia finished off Croesus, the Ionian cities were knocked off one by one over a fairly short period. The Anatolian languages vanished pretty rapidly after the Persian conquest. The Persians, oddly enough, adopted Aramaic as the standard language for the empire. That was a lucky break when it came time to crack written Persian.
There is no known relationship between Sumerian and any other language; same goes for Elamite; same goes for Dravidian, although it isn’t unlikely that they are relatives of the Harappans (the written version of that language remaining unread). Trying to link living agglutinative languages has been problematical (it used to be that Turkish and Korean were thought to be mutually closest living relatives).
Arzawa
http://www.freerepublic.com/focus/chat/1289143/posts
Lycian Influence To The Indian Cave Temples
http://www.freerepublic.com/focus/chat/1440990/posts
On a mission to explore deepest Lycia Where Greek language has left its mark
http://www.freerepublic.com/focus/chat/1549447/posts
Genetic link shown between Indian subcontinent and Mesopotamia
http://www.freerepublic.com/focus/chat/3073191/posts
http://www.omniglot.com/writing/lydian.php
https://www.lib.umt.edu/lang/smalfamh.htm#Etrusc