3 Weeks of OM-D, 3 Weeks of Rubbish

If your E-M5 produces normal, sharp images when shot off a tripod, then the problem is likely due to too slow a shutter speed for the focal length you are using, i.e. ignoring the 1/focal length fule.

And shutter vibrations (if there are any) are usually so minor, and happen for such a small percentage of time of exposure, that they don't register in any noticeable way in images.

Besides, if images are sharp when you shoot from a tripod then it's likely that shutter vibrations are not the problem.

If you want to isolate any problems you need to be extremely methodical in your tests. Fire from tripod, if images are sharp try handheld but with super fast shutter speeds. If images are sharp, test slower shutter speeds to find the slowest you can handhold an get sharp images, etc. Good luck.