Thats quite a range of occurances.
Has anything been modified on the car? By the way what car are we talking about?
Its pretty hard to diagnose car problems over the net since weve no idea what the sound is like or what shape the car is in.

If youre mechanically capable Id throw the car up on jacks and check the following.
- take wheels to get balanced and checked for damage (ie: bent rim bad radial run out)
- arm bushings
- grab a dial out indicator and check rotors (if they are in bad shape itll tell you theres a wheel problem)
- bust out the impact driver and check out the wheel bearings like Rocky suggested.
- check caliper mounts make sure they arent loose

I want to just blame your problems on bad wheels (bent hubcentric ring problem...) but with the noise happening on acceleration and the car sounding like its falling apart going over bumps Id like to blame the bushings. If youve torn a bushing the ride can get pretty nasty and loud. Usually this is easy to spot since the suspension gets sloppy and biased. Not too much we can do over the computer.