Data Transfer always involves two components: An export process and an import process. Both of them need to be aligned with each other to produces a correct result - or at least a desired one. Now, we don't have your source files available, but let's tackle your comments bit by bit:
Another weird thing is that the .OBJ file is 920MB in size
This is basically buried in your tessellation settings. Your model is an architectural one, meaning it spans across a dimension of roughly 100 meters. Rhinos internal units however deal with sizes of millimeters or centimeters (to be checked within your Rhino settings), and the tessellation refers to that. The defaults are crafted to objects at the size of a coffee machine would tessellate nicely. You're feeding something considerably bigger to it, so the settings for tessellation can be lowered to compensate for that. Especially the minimum edge length seems to be far too fine from where I stand. As soon as objects are curved, this will result in very dense triangulation.
But when importing to Blender nothing shows and layers don't work either
The first part is a misconception. Check your own screenshot and have a look at the right on the Outliner area:
You'll notice that there are a bunch of objects. Generally that means that data has been transferred, just you don't see it. And this leads to the second part, which is:
OBJ sucks at what it actually CAN store
OBJ has no definition in the file format for layers, as has been mentioned in the comments already. You will only get as far as achieving at least that things come in as more than one object (which is the case for you already), but that's about it.
Worse than that, OBJ has no means of storing units. That means, when you try to store a vertex located at
(1.0, 0.0, 0.0), OBJ will happily write down the numbers, but not what
1.0 actually means. Millimeters? Meters? Feet? Inches? You won't know. So what breaks in your scene is that Rhino exports the numbers very likely as millimeters, but Blender on the import side interprets that same raw numbers as meters. This results in your scene scaled up by a factor of
1.000, too big to see it in the viewport.
The worst part however is that the OBJ importer in Blender has no
Scale setting either, which you could use to apply that unit compensation. Blender 2.82 does have it for the exporter, but not for the importer, for reasons that are beyond me. So the only thing you can do on the Blender side is to scale down the scene using the 3D Cursor as the origin by a factor of
1.000. Maybe you have said unit compensation on the Rhino side.