Steering wheel shaking issue

The first thing to try would be to rotate the tires and see if the shake lessens or transfers to the chassis. If it transfers then the tires and wheels need to be examined for damage, out of round or balance issues. Any of those can cause shaking. If rotating the tires does nothing then the front suspension and bushings need to be checked to see if they are worn or damaged. If the rims are the style that stick out of the fender well and have low profile tires they are very easy to damage with potholes, curbs or road debris. Ply separation in the tires is also common due to the same things. Even a small amount of imbalance on them will cause large problems because the weight is out beyond the steering center line and can act like a lever to move the tire like a pendulum.
So I would start with the rotation.