Enya Shrine is the tutelary shrine of Izumo and is located south of downtown. It used to be called Yamuya Shrine, and the main kami enshrined is Yamuyahiko and his wife Yamuyahime.
Yamuyahiko was a grandson of Okuninushi, and other than that I can find no information about him.
The shrine is very old, being listed in the Izumo Fudoki of 720, as well as the Engishiki.
Also enshrined in the main shrine is Kotoshironushi, Oyamazumi, and Ojin,.... a strange mix of kami. Enshrining Ojin makes it a hachimangu, though it is not officially named that, it is considered the number one of Izumo's eight Hachimangu. Hachiman must have been enshrined here much later.
Secondary shrines within the precincts are to Inari, Tenjin, and Aragami, among others...
There was a nice pair of small, wooden komainu in the Zuijinmon.