Ali Al-Chalabi brings up a good point. Some tires have relatively soft tread compounds, mainly those that are skewed to provide better traction, at the expense of wear life. These tires also tend to be used by owners who think they are willing to give up ride characteristics for handling. A by-product of this is that they are often on the low end of inflation pressure to improve ride charactersistics in normal driving. Additonally these kinds of tires are susceptible to taking a set overnight in their at rest shape. Look at the tire at rest and it has a flat bottom. Initially these tires present a flat surface to the ground on every revolution, until they warm up and centrifugal force helps them go back to being round. The will vibrate as a result. The longer they sit the worse this can be.
But that does not address your pulling to one side issue. Is the pulling always to the same side?
Next time you take a drive for a dozen or more miles, when you get out check the temperature of the wheels on all four corners. Be careful as if you have a grabbing brake, that wheel might be very hot. A visual indication is if one wheel is getting dull and more rapidly aging the paint on the alloy wheel. If this is the case, you will need a new caliper or two, or you can have them "rebuilt" which means have the seals changed. When the piston to cylinder bore square shaped "O" ring gets worn there is no longer any mechanism to pull the pad away from the rotor after you release the brake pedal. As a result the pad stays in contact and heat the whole area up while you drive. The result is rapid wear of the pads and rotor on the aflicted wheel or wheels.
I am not sure the pulling and vibration are directly linked. I would suspect the tires/balancing for the vibration and the brakes for the pulling, assuming you have no bent front end or rear suspension parts. Good luck and I hope this helps. Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)