This may not be too much help, but I know the W124 power steering system will "hum" through the steering wheel when its low on fluid. This happens routinely to me because I have a really slow fluid leak. So, when it gets low I get that familiar vibration when turning. But typically it doesn't matter the direction being turned.
As a relatively inexpensive thing, first, you could check the fluid level. The owner's manual should show you the fill line indicator.
Second, you could try changing the power steering filter. This may be effective - especially if you put on a used pump. The power steering filter is held in by that center post in the fluid reservoir. It's a doughnut shaped thing in the bottom of the reservoir tank.
Do you happen to know what kind of fluid you are running in the system? I like the newer power steering fluid that is more like a hydraulic fluid (its clear) than transmission fluid (red). Havolene Power Steering Fluid.
1982 300D at 351K miles
1984 300SD at 217K miles
1987 300D at 370K miles