*do not double post!*

The part you are talking about is called the bridge. Apparently it is a tremolo(whammy bar) bridge since it moves. Are the new strings a heavier gauge than the old ones? That could be the cause. Only thing I know to do is look at the back of your guitar. You should see a removable plate in the center that when removed exposes the under side of the bridge and some springs. One solution might be to move the springs around so they create more tension on the bridge, or you could add a couple of springs.