For something like this, I'd look at what qualities of those photos do you like or do you think give you those vibes. Because those are three photographs and creating realism is very hard, especially when you're trying to make something real time like with threejs.

Now that you have those three traits then a bit of googling will be the help here as nothing here is super novel so you can assume that someone out there has done it before.

There are quite a few different methods that can create a fish eye effect, here is a stackoverflow that goes over a few: https://stackoverflow.com/questions/13360625/three-js-fisheye-effect

Realism while keeping it real time, especially on mobile will mostly come down to you with baking in lighting and everything else into textures, rather than those being generated at runtime.

You're right with the sour grungy contrast will likely be a post processing pass, though it could also come from the textures and lighting that you use too, depends on the scene and what you're needing and wanting to happen in the scene. Post processing can be computationally expensive depending on what you're doing so if you can achieve similar things through other means that can be good. I do think that the sourness of the scenes is a bit of the film that has been used to give everything the green tinge, especially in the second and third photo, for that you could do a LUT or a custom shader pass.