First:Shake like that could be caused by wheels being out of ballance. I believe it's important that it be done on a computerized system IE: Hunter Balancer. Second: the suspension (tie rods etc) need to be inspected. Third: Bad wheel aligntment can cause different types of weird tire wear that can cause vibration in the steering wheel.

Abnormal wear in the tires can vary. I had vibration in the steering wheel on another car and went through the whole process. As it turns out the wheels were out of alignment and caused wear that was not visually obvious. I can't remember the term but each tread block was worn slightly uneven from front to back. The only way you could notice it was by running your hand lightly across the top of the tire from front to back. You could feel an edge at the begining of each block. Conversely a correct tire would feel smooth. You could feel it but you couldn't see it.

A wheel alignment and moving the tires to the rear solved my problem but not untill I spent $$$ doing everything else. The people ballancing my tires didn't even think of this.

As far as special stuff to check on MB ????