Speakers in car cut out at higher volumes? Sound is distorted?

Ok so I have a 1997 Honda Civic that's in good shape but the sound is trash. Anytime the the music is at a low volume it sounds fine but at meduim or high volumes the sound is distorted. I thought the speakers were the problem so I replaced the ones on the door but it sounded a little bit better but really about the same. What do I need to have louder speakers without the distorted sound? A new head unit? A subwoofer? A new amplifier?

What new speakers did you fit I recommend fusion speakers and don't by any aftermarket speakers with less than 100w

Any stereo can sound no better than its speakers. Find some speakers at a stereo shop where they let you listen to them before you buy them. Replacing bad speakers with more bad speakers is what you've done.

You're probably trying to overdrive the speakers with a puny amp that doesn't put out enough power. That "cutting out" is called "clipping", which will damage the speakers, if it hasn't done so already. And, trying to drive your sound system too hard can cause the amplifier to overheat too with potential negative consequences. Since you obviously want more loudness you require an amplifier for the car speakers, and if you want significantly more bass you'll also need a subwoofer, although many 6x9 full-range speakers put out pretty decent bass. Without knowing anything about your present equipment (number, brands and models of speakers, brand and model number of stereo head) it isn't possible to advise you further.