I'm wondering if Satin would allow me to create a distortion shader located at a specific point in the world, or if it only supports camera shaders. I can't really use Canvas as an option, which I know supports them, as I need something that works with Sodium, which I'm hoping Satin works with.

Depends on what you want to do, but you can use the depth buffer in your shader to render things at specific locations like the depth example mod

Specifically I'm wanting to add it to an entity. I'll take a look at the depth example, though. Thanks

If you want to make an entity render with a shader, you can use the render layer helpers, like the render layer example mod.