This Nogi Shrine has absolutely no link to the more famous Nogi Shrine in Tokyo. That one is a twentieth century creation enshrining the "patriotic" General Nogi who committed suicide following the death of Emperor Meiji.
This Nogi Shrine is named after the ancient district of Nogi in Izumo, and is much, much older being listed in the Izumo Fudoki and the Engi Shiki. It was one of the top three shrines of Izumo, along with Kumano Taisha and Sada Shrine, up until the 11th Century when Izumo Taisha was promoted.
The main kami is Amenohiho, the first emissary sent from Amaterasu to convince Izumo to cede their land to Yamato. The Yamato say he joined Okuninushi and didn't report back. The Izumo say he did report back and his son came down to pacify the local kami. Amenohiho is considered the ancestor of the high priests/ governors of Izumo.
There are numerous smaller shrines within the grounds as well as a couple of altars to Kojin, the local land kami represented as a straw snake. Also enshrined here is Onamuchi (Okuninushi), Kotoshironushi, Hachiman, Futsunushi ( the tuteary kami of the Mononobe who played a part in subduing the local kami).
Also enshrined are Kuninotokotachi one of the primal kami of creation, Kuninosazuchi, an earth kami, Izanami, Tamayorihime, Juntoku a thirteenth century Emperor, kamusubi, Ayakashikone... a kami produced before Izanami and Izanagi who I had never heard of before, an Atago shrine, and an Inari shrine.