This is the front end I presume.The talk of link bushings sounds more like rear end suspension.
The noise you describe sounds like loose wheels bearings. I can't imagine the strut making any noises under hand loading unless the piston has totally come apart (this would be extremely apparant from both the negative camber it would cause and the horrible racket it would cause on the road.
This strut holds onto one quarter of a 3000 lb automobile at high speeds and severe dynamic loads. If you can affect it at all with your hands can you imagime what it would be like on the road.
If you can feel play look for what is moving the first line of control is the wheel bearing adjustment, next the lower ball joint (can't be checked by hand either - needs to be supported by lower control arm and the the wheel can be lifted with a lever to see the play). The easiest play to be felt by hand (after the wheel bearing) is the steering linkage (they can get very loose but the only noise they make is if they are rusted tight - and squeek). The idler arm bushing also can be felt by hand from the passengers side. All the linkages should actually be check on a wheel lift so they are in the driving attitude. When hanging from frame lifts (or on jacks stands on the body) the tierods can be under tention or in an unworn angle which can hide the play).
Other than stabilizer bar links there are no links with or without bushings in the front suspension that play can be felt by hand. The lower control arm bushings almost never are a factor on 124 front ends.
The rear end links are a different story. Many can be tested by hand with a little aid of a large screwdriver/pry bar.
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician