Well.. (after converting from metric) you're saying that the speakers you have are 5.25" and 4"? Then those speakers are your problem. They're too small to give you any real bass. And with such meager power handling (20-25 wrms) that means they will distort easily when you turn up the bass. Using an external amp would only make it worse. A new head unit won't help either.
First, get better quality speakers that can handle more power. You can set your bass controls up higher then without distortion. After that, consider adding a sub and amp somewhere. Even an 8" subwoofer can make a world of difference to an otherwise inadequate system. If you do that, you can put bass blockers in your main speaker wires so you can turn them up even higher.
If a sub isn't an option, see if you can fit bigger speakers into the car somehow. Replacing 5.25's with 6.5's makes a huge difference.
1999 Buick Park Ave Ultra
Head Unit: JVC KWHDR720
EQ: Audiocontrol EQL
Front Stage: Hybrid Audio Technologies Imagine 5.25 mids, Morel Maximo tweets
Sub Stage: Boston G3 10", 0.5 cu ft sealed
Amp: PPI Phantom 900.4
Rear Fill: Boston SE953 6X9's