Do you think you could provide a screenshot of your my_objects folder? It will be easier to spot an issue in there visually than have to guess.
I don't see anything unusual there. Maybe I could suggest you take them all out of the my_objects folder (as well as the installed .object files in the objects folder) and put them in a new folder on your desktop. Then, add the different objects in the my_objects folder on by one (Example; thing.mesh, thing.material, thing.png/.jpg) and see if there is a particular object that is causing all of these issues. If so, you might have to remove that particular object and maybe try to get the original download back and try again to correct it.
If that doesn't work then we'll just try to look into it further.