Sounds a lot like the sway bar is rubbing the subframe or the control arm.
I have had mine rub the subframe. Turn your tires one way (to full lock). Go up front and look into the back of the front wheelwell, towards the engine. Find the sway bar, rub your hands along it and see if it is touching. If it is, pull hard. If that side is fine, check the other.
The strut won't really make a noise, unless all of the parts for the valving have fallen off. You would hear the strut rod rubbing, but you wouldn't be able to drive either.
An engine mount will produce more of a thump. My brother has that problem in his car now.