Spray starch your fabrics before cutting. When we do a block exchange I can always tell one friend's block, because it would stand up by itself (heavily starched), and it'll also be perfect. Down side of starching your fabrics: You will have to wash your quilt when it's finished.
Personally I don't mind a little 'movement' here or there. One of the reasons why quilting appeals to be it because fabric is so tactile.
If your pieced strips don't lie perfectly flat, and you don't want to undo the seams and start again, you could try and press them into submission with a steam iron. That quite often sorts out the problem.
Lorchen