Elda is an elf who was summoned to earth to be Takamimi Shrine's patron goddess during the Tokugawa shogunate. Hundreds of years later, she's a bit of a recluse, too shy to speak to her parishioners directly. She's also lazy on top of that, more inclined to stay at home playing video games and making mecha models than to do her work for the shrine.
Parts of this manga are really cute. Koito, the new priestess of the shrine, is both Elda's best friend on earth, and a frustrated foil. At sixteen years old, she's much more serious about her responsibilities to the shrine than Elda is, and she has to go to school on top of that. Koito's sister Koyuzu, and her schoolmate Koma, round out the fairly small cast, and give us an opportunity to see how Elda is torn between her naturally shy nature, and wanting to experience more of the world beyond watching TV.
Otaku Elf has a mild edutainment vibe, not dissimilar to what I saw recently in Tamamo-chan's a Fox!. This time it's about Chuo City, or is it Tsukishima? I'm unclear about which is the larger-scale area just from reading the manga. The area that Koito and Elda live in is shown with detailed backgrounds: its waterways, high-rise apartments, the restaurant districts, et al. We get some lightly-presented information about the Tokugawa era's history, the cuisine of the area around the shrine, the use of lanterns and candles long ago, and a few other things like that. It isn't as detailed as in Tamamo-chan, and doesn't give the reader as much of a sense of place, in my opinion.
I don't entirely see the point of either having an elf in this story, or of making her an otaku, which kind of nullifies the title in English, at least. Elda could have been an actual goddess and been lazy, and it would have worked just as well. Also, I don't have a good sense of their neighborhood, or the prefecture, or whatever it is, as a community with human beings living and working in it. There are few or no background characters to fill things out, making the area seem oddly empty and abandoned.
This is fun enough to keep on with, but it doesn't quite have enough going for it to really make it stand out.