Try exporting to Collada dae and importing into blender. I dont think it matters what format you're using to transfer between the two, just make sure its something that works. I've used this format from blender to sketchup but not sketchup to blender so idk.
Im wondering though, if when you export to obj and then import in blender, it's only saving the triangles and none of the vertices and edges? Since it finds no triangles it doesnt save anything