Incorrect air pressure in tires can sure cause symptoms. Shocks and struts might help a lot. Also check ball joints, both inner and outer tie rod connections, and bushings. The bushings at the rear of the front control arms go bad a lot. Track rod bushings, if bad, would cause side to side slop in the rear, like "twoforty's" said. Front sway bar bushings should be examined also.

If you decide to do struts, here are some directions that might help. Other posters will have different approaches and maybe some corrections or suggestions, but this method works well for me.

Also see Strut Replacement Procedure, 720-2, 720-5 Bentley. If you are not careful, you can get hurt or worse. Don't rush or drink beer while doing this job. Pay attention to what you're doing. Have a helper on hand the first time. These directions don't cover every single thing and assume basic DIY skills and safe shop procedures. The job might be a lot more difficult if your car is rusty, especially if the gland nut is corroded and stuck in the strut tube. How's that for a disclaimer?

1. With weight of car on the ground, loosen top nut 1 turn with special tool or air wrench. Do NOT remove.
2. Put car on jackstands, at least the front.
3. Remove front wheels.
4. Loosen strut gland nuts.
5. Remove end link top nuts. 17mm socket
6. Remove brake line bracket bolts. 12mm socket
7. Remove inner brake line clamps. 8mm socket
8. Disconnect tie rods. 18mm
9. Loosen fasteners for front and rear A-arm bushings.
10. Put jack under A-arm near wheel.
11. Release then remove 3 nuts on top of strut tower under hood. 13mm
12. Lower strut assembly to outside of fender.
13. Support assembly with two 3/16 rod special hooks into sway bar hole.
14. Compress spring SAFELY. 3 coils between jaws of compressors.
15. Remove top strut nut.
16. Remove bearing mount, spring seat, spring, bumpstop/boot.
17. Remove strut gland nut.
18. Pull out old strut, compare length to new, put in new.
19. Tighten gland nut. Use NeverSeize. The gland nut might not fully seat. You might see a thread or two. That's OK. New strut insert should be tightly held in tube.
20. Clean spring seat.
21. Install compressed spring, bump stop, spring seat, bearing/mount.
22. Tighten top nut (15 lbs) using Lisle special tool. Don’t spin strut rod inside strut.
23. Release spring compressors CAREFULLY, making sure spring is seated properly.
23. Raise strut assembly into strut tower while guiding end link into sway bar.
24. Torque top 13mm nuts to 15 pounds.
25. Tighten gland nut some more.
26. Torque tie rod ends to 44 lbs. with Loctite.
27. Put weight of car on wheels. Bounce car a bunch.
28. Torque front and rear A-arm bushings.

If you haven't done the job before, this might make it sound more difficult than it really is.

Thanks for all the help,
DougC