your speakers could be blown, if the cone moves freely when you touch it, it's probably blown. you'll have to get new speakers.
your head unit (the part you control the radio with) may be too old and underpowered to power modern speakers, it's best to buy a new head unit and new speakers at the same time.
If you want clear sound at very high decibel levels, you're going to have to spend some money and buy premium speakers and an amp to drive them.