Porl, I'm hoping that part of your description was a mis-type - Both in the USG manual and in my various posts on construction, I tried to make it clear that fastening ANYTHING to WOOD studs, requires Type W, as in Wood, screws. If you've already used Type S (as in Steel) screws, did you notice any tendency for them not to grip well? If not, you may be OK. Still, it makes me nervous.
As far as the screws for the rest of the layers (ONLY on the side with the Resilient bar) you should just use longer Type S screws for each layer, offset so they don't collide. Putting a strip of wide masking tape on the floor and making notes/marks will help keep track - if there's anything to fasten tape to at top of wall, do it there also - otherwise, a plumb bob will help keep things in line. When screwing the layer of MDF, if the screws don't sink flush you may need to use a countersink first, and make dimples where the screws will go. Make these just deep enough to cause the screws to sit flush.
For the OTHER side of the frame, you'll be fastening the first layer directly onto the wood studs using Type W, not S, screws - subsequent layers will need the special Laminating Screws USG calls Type G (for Gypsum) - I couldn't find those anywhere in my area yet, so that may be a problem. The reason this needs to be done, is that you do NOT want subsequent layers screwed directly to the studs, because the studs are not flexible enough to absorb the sound that travels along the screws. For this reason, you want to run 2-3" wide stripes of joint compound parallel to, and about 2-3" away from, the studs - then place the panel on spacers (same as all wall construction) so as to leave a gap between floor and wallboard of about 3-4mm - fasten the second panel to the first using the Type G screws in line with the stripe of joint compound, so that each panel has a line of glue and screws offset slightly from studs, repeated near each stud.
What this does, is to fasten the panel without passing sound directly into the studs. The glue and screws give strength, and even though the Laminating (Type G) screws pass thru the panel they do NOT contact the stud. What sound gets thru the screws is absorbed by the insulation/air space.
A third layer should be done the same way as the second, but with screws offset vertically ONLY, to avoid collisions between fasteners.
Once the all panels for a particular layer are fastened, pull the spacers out from under them and caulk thoroughly before doing the next layer. Never put two layers up with seams coincident - offsetting by one stud spacing, both horizontal and vertical, is good.
Here's sort of a synopsis I eventually will expand on, that covers a lot of points - The first #5 re-visits part of what I wrote above -
http://johnlsayers.com/phpBB2/viewtopic.php?t=598
I still need to find some time to research this scarcity of Type G screws - I hope you have better luck than I have so far. Try asking for them by the name Laminating screws, or Drywall Laminating screws - If you can find a local Drywall contractor they may be able to help. Look on page 40 of the USG Construction manual for definitions.
Page 118-119 of the USG manual cover part of strip laminating for sound control. You do NOT want to fully laminate layers, the difference in Resonant frequency of each layer improves on sound isolation so each layer needs to be (somewhat) free to vibrate on its own. That's why the strip lamination on wall leaves that attach directly to wood studs.
Hope that helped... Steve