If a ball at rest is moved by another ball, it is replaced and there is no penalty to the player whose ball was originally at rest. The player whose ball in motion caused the ball at rest to move, plays his ball as it lies and there is no penalty. Except, that if both balls originally lay on the putting green, the player who struck the ball takes a two stroke penalty.
So to answer your questions:
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so you lay me a stymie. i'm planning to chip over your ball and hole mine out. but, my ball lands on your ball, moving your ball further from the hole.
how's this played? do you play it from its new position or replace it?
what about me? penalty?
The ball originally at rest is replaced. If both balls originally lay on the putting green, you incur a two stroke penalty. You play your ball as it lies.
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i read something about knocking the your opponent's ball in and this just meaning that he'd holed out. this leads me to believe that in the situation above you'd just play it as it lies. but, i'm not sure. and if that's the rule, you have incentive to hit your opponents ball away.
Assuming I am remembering this correctly, it is irrelevant if a ball is knocked into a hole. It is replaced and the any applicable penalties applied.
See Rules 18 and 19 for balls at rest or in motion moved.
See also Rule 22 regarding a ball interfering or assisting with play.