Sounds like you need new tires. When they get old, the steel belts will separate from the body of the tire, causing the tread to deform. This will reduce the amount (width) of rubber on the road, and cause the problems you have. They also vibrate.
Cheapo tires will cause the same problems, make sure you have at least H rated (130 mph) tires from a good manufacturer. Off brand low cost tires don't belong on these cars!
And check the inflation pressure, too -- overinflated tires will also have very little tread on the road, very dangerous.
Your Benz should track very nicely at high speed, and you should have decent traction in wet weather -- not superb maybe, but decent.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!