This is usually a symptom of excessive run-out (warped) on front brake rotor or rotors.
Tires,inner tie rod bushings, if the steering wheel shakes when brakes are applied - brake rotors warped.
If you change the suspension geometry (which you did if the shocks weren't the exact same size/grade/damping) then you might have to take it to a professional. There are just too many variables, like power steering, steering fluid, brake fluid, brake disks installed properly, ect. Go to someone who knows what they are doing is my suggestion.
check the rotors they could be warped
the brake rotors are warped. resurface or replace rotors. if the vehicle shakes without applying the brakes, check tire balance.
go get 2 new tires and have the alignment checked on it
Rotors out of round - should be resurfaced or replaced
You need to check rotors and brake pads one or both are failing.
If 4x4, replace steering dampner that is a bandaid, is not addressing the real problem. could be worn or bent steering parts, bad ujoints, out of alignment or bent or unbalenced wheel.
Need some more details. Vibration all the time? Only certain speeds, only when you accelerate, vibration in the steering wheel, in the whole vehicle?
Chattering/vibration at all speeds. Chattering when brakes are applied. Poor fuel economy. Noise.
prob a broken belt in one of the front tires
This depends on a few things: If your vibration is happening at high speeds, get your wheel balance/roundness checked if this is happening at all speeds, check your alignment/steering if this is happening when slowing down, chances are that you need new brakes