I did experience the exact symptom you mentioned in my W201 190E....

Replaced both tie rod ends and ball joints and adjusted the steering box (too much free play). And did a 4 wheel alignment.... Cures the wandering straight away...

From my experience....a worn shock will cause the car to suffer from a bumpy/bouncy ride while a worn strut top mount will create thumping/clunking noise when driving on uneven roads....

I would recommend you check the tie rod end, ball joints for front and all the bush and control arm linkages at the rear....