2000 Dodge Caravan car gives me headaches due to shakes

When I drive fast,70- 80mph, car starts shaking too much. Everything inside the car shakes a bit, coins jingle, soda can in cup holder shakes incredibly. The steering wheel shake is almost imperceptible, but constant. When I drive 20-40mph, if the roads are perfect, hardly any shakes. But on average roads,(fwys in so. calif.) car shakes a bit, all the time, and gives me headaches. So I can't drive my minivan to work, because it gives me headaches. Also, when I drive, I feel every flaw on the road too much. Any ideas? Someone suggested that I should replace the axles. I had the shocks and struts replaced, and four new tires.