Iya Shrine is a very ancient shrine, said by some sources to be the oldest shrine in Izumo. It is listed in the Izumo Fudoki, menstioned in the Nihon Shoki, and listed in the Engi Shiki. It is one of the "Six Shrines of Ou", Ou being the old name for the district and the site of government in the Nara Period.
The primary kami is Izanami, and near here is the entrance to the underworld (Yomi) where her husband/brother Izanagi fled from after visiting her there. Also enshrined here are Okuninushi, his son Kotoshironushi whose main shrine is across the lagoon at Mihonoseki, and Sukunabikona a sidekick of Okuninushi who "built" the country with him.
The third layer of kami enshrined in the main honden is Takeminakata, the son of Okuninushi who didnt't want to cede the land the the emissary of Amaterasu and who is the main kami of Suwa shrines, and Futsunushi, the ancestor of the Mononobe who was the emissary from Amaterasu.
There are some secondary shrines in the grounds including two Ebisu shrines and a Tenmangu, but the most interesting is the Karakuni shrine. Karakuni means "Korea", and there are quite a few of them in the Izumo area, and they enshrine Susano and his son Isotake. According to Izumo mythology they both came to Izumo from the Korean Penisula and also made visits back there, something that is widely ignored by the nationalists here.
There is also an altar to Kojin and an Inari shrine, but I will post on them next.