The truss rod is a metal rod that is bowed in the center of the neck... So pretty much on torquing (twisting) of the neck is torqueing with the truss rod in no position to counterbalance the torque. Truss rods adjust the neck bow straigh forward and straight back... so it's not going to do much for you.
It doesn't make much sense for the e and the B strings to be the side of the twisting because normally the twisting occurs on the E and A side... Because there is much more string tension on that side of the neck and sometimes that can be counterbalanced by adjusting the truss rod and using the strings as the counterbalance... Using a lighter gauge set of strings on the bass strings and a higher gauge set of strings on the treble strings... Within a few months of that the neck should be straightened out in that case... But you can't really do that with your because it's your treble strings that are on the high side of the torque..... I'd say have a tech look at... It's always hard to give really great advice about a guitar that I can't see and touch and inspect up close... Take it to a tech and see what they have to say about the neck twisting... Getting a new nut installed or having yours refiled may solve your troubles though. Normally that twangy sound comes from strings that are getting pinched in the nut. As your strings sit in the nut the cut into it and burrow their way into the nut creating a pinch or pressure point for the string. What you can do is either totally replace the nut.... Or you can have a tech refile yours. Doing a refile will obviously be less costly. What they'll do is go in with some nut files and file in a proper seat for the strings to sit on and move freely through the slot when the trem is being used. It will help with tuning efficiency as well.
Hope this helps a bit... I'm sure that LATS will have some input as well and I'm positive there's something that I've probably missed... It's towards the end of the day and I'm ready to go home. haha.
Good Luck.
