The centering while driving is castor angle related. For instance pull out of a side road onto a main road and let go of the steering and the car should straighten out on something like the correct line, if you have to pull the steering back straight it needs a steeper caster angle. Its not officially adjustable on the omega, but it can be tweaked by moving the entire front sub frame forward and back.
However, the fact your only really feeling the symptom when moving slowly, and i guess with a fair amount of steering lock applied? May well mean that the camber is not set correctly. This is set by the 2 bolts at the bottom of the shock which are ovalised allowing the hub to lean in and out depending on the correct settings. If you watch the wheels when you turn the steering from lock to lock when stationary, you'll notice they lean over a noticeable amount, and the front of the car will move side to side as you move the wheel. In this full or extreme lock position camber angle also has an affect on the caster centering sensation of the steering wheel in your hands because of this leaning as i understand it.
Shock replacement does not involve undoing the sub frame bolts. So the caster angle will not have altered. But the camber will, without a shadow of doubt, be wrong with new shocks fitted. I strongly recommend full geometric set up, before you drive anywhere else, or your tyres will wear unevenly and become "geared" to pull one way or another. This "geared" shape to the profile will then affect the tyre for the rest of its life meaning even when set up correctly the car may still pull left or right until the tyre is replaced. Hth :-)