The "twanging" noise you are refering to is due to the fact that on coilovers the springs arnt locked into place as they are on normal suspension which means the springs can move round 360 due to the adjustment side of things. The problem this causes is that grit and dirt can get in between the springs and the spring seats, also it can get in between the large spring and the small spring at the bottom (depending on what make coilovers you have) and this causing the springs movement to be jurky and not smooth when turning. So basically as the spring moves round with the wheel when you turn it catches on a bit of dirt and gets stuck, then as you turn more it forces the spring to move round so it then jurks round causing the twang noise. It happens at low speed end if you turn the wheel when stationary. The more crap you have stuck in there the worse it will be.
Now how to cure the problem.... get ur car up on the ramp and remove the front wheels so you can see all of the suspension, then turn the springs round with your hands and you will feel all the grit in there as it wont turn smoothly, so spray the areas where the spring touches anything, ie. the spring seats etc., as best as you can with brake cleaner or degreaser etc. to get the worst of the crap out (You will see all the formentioned crap on a visual inspection of your springs) Try turning the springs round after you have cleaned them to see if they move any better. Then what you need to do is get some grease on a brush and put it in the places that you have just cleaned, try to really get in between the spring and the seats etc. try moving the spring round while your putting the grease on this may help. Dont be shy with the grease either because it needs to stay on the springs while your driving the car as this does not cure the problem instantly, it may even take a week or two for the grease to work its way between the springs and into the crap, it basically turns the gritty crap into greasy crap so it doesnt effect the movement of the springs. Now i had this problem and it worked for me and a few of my mates but im sure it wont work for every one and it will only cure the twanging, it wont cure the knocking some of you have. As i said before it wont cure it straight away so bare with it for a while then one day it will just stop and u wont even realise. I hope this helps.