Well, the power handling of the speaker has nothing to do with your problem. First, double check the connetions to make sure everything is in phase, swap the +/- to check polarity.
The other major problem is you are running aftermarket speakers which are generaly less efficient(although much better) than the stock speakers and your stock radio doesn't have enough power to run them. When you turn up your stock 11watt stereo you start to clip the amplifier, which is basically like running beyond redline like in an engine, Less power, less efficient, more heat, more likely to explode.
You will notice a HUGE improvement with a new head unit and/or amps. It will sound clearer, more accurate, better tonality and you will be able to turn it up much louder with the same clarity without blowing up your speakers.
RULE No 1: You can never have too much power. People blow speakers by overdriving their amps not the speakers.