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...but when it comes to a straight & unlevelled road, the car just behaves abnormally.
How low is it? It could be bump steering, although the fact that you say it somes from the rear is a bit confusing. If the car is steering itself when hitting bumps (steering wheel jumping to one side) and your car is low its likely its bump steer and could be helped by adding roll center correctors (a spacre which goes between you steering arm and the bottom of the strut.
Also get a alignment as suggested and get them to measure the toe on the rear. Ideally you want a little toe in on the rear (about +.5mm per side is good) if you have to much toe out it could make it a little unstable but, again that *should* show up in cornering with it feeling a little tail happy. Like DD said it could also be castor, I'm not sure what they came with factory but about 2 deg castor is a nice compromise between steering feel and handling. 3 to 5 degrees and steering will get heavy especially if you have a smaller steering wheel. It does however help handling and stability alot and you also get the added bonus of less turn in understeer
Sorry I can't be more helpful but thats all I can think of at the moment