Brauner,
I run 18" with 225 on all fours.
The reason for your car 'swaying' is due to the lower arm bushes. Check if you have the stock bushes (ones that have holes in them) and replace them with M3 type bushes (they are full hard rubber and no holes).
The swaying is due to the weight of the 18" rims. The stock lower arm bushes are good for road handling for 16" & 17" only.
A ccol looking width is 225 or 235 (max). My opinion. Further, after you change the bushes, do get the wheel alignment, balancing, camber and caster settings done for you car.
I believe the car sways, when you apply the brakes too. Good Luck.