D&J would know this better than I, but it sounds to me as if one possibility is that your steering is all out of skew.
Have you (or anyone else who drives the car) clipped a kerb or even smacked one? Do you drive over a lot of potholes or speedhumps (at anything more than about 5mph)
If you have the wrong camber and/or caster on a wheel, then it loses it's tendency to want to straighten up and when steered in one direction it will want to steer more (i.e. it is unstable)
The camber and caster could be messed up through even a minor collision with something stationary. Perhaps try looking at the car, when parked on a flat surface, with the front wheels facing straight ahead. They should both tilt in a tiny bit towards the top, and both face exactly ahead. Then try turning the steering all the way to the left, have a look at both wheels (or even better take a digital picture). Now turn the wheel all the way to the right and compare. Look for any oddness (i.e. if when turning right the right wheel seems to be tilted in comparison to the left wheel when turning left).
There are other possibilities too, but I think this is a good first check.