I have experienced similar issues with my 2005 SR5 and it has been driving me nuts but I have, at least in my case, found a real solution. My problem started as a simple bump or clunk after I released the brake pedal following a stop. I thought it was coming from the front of my vehicle while passengers insisted it was coming from the rear. Later on it transformed into multiple sounds that I would notice while driving and sometimes even turning. I thought I was having multiple issues from brakes, drive line to shocks or struts. The new sounds even sounded different more like a boink or clank.
I saw posts suggesting this noise would be resolved, albeit temporarily, by lubing an area near where the drive shaft and differential come together. To me this seemed like an odd solution but was willing to try anything. So I took my vehicle to two mechanics and mentioned this solution to them and both times received the same response. There is no place to lube in or around the drift shaft or differential, they are both sealed. Regardless they checked and confirmed what they already knew.
I also had an extensive conversation with another 4Runner owner who was able to win a lawsuit against Toyota under the lemon laws. He insisted that the noise was coming from something internal to the differential; it was called an impeller or something like that. He also said that there was a TSB for the Lexus LX which explained the issue. I was unable to find it.
But before I started down that path, I took my vehicle into a mechanic and paid for a $14.95 vehicle inspection. As which point, they told me that everything looks great with the exception of a motor mount that was going bad. Needless to say, I was doubtful this was the cause of my noise issue since they were multiple noises coming from different places with different sounds, but I decided to go ahead and get it fixed anyway. AND IT WORKED!
Here’s an explanation: Imagine when you come to a stop, momentum causes the motor and drive train to lurch forward. Normally if there isn’t anything out of whack like a motor mount, the motor and drive train and everything connected to that system would quietly move back into place. However, because the motor was displaced at larger distance than is within tolerances, things like the drive shaft would bind and not move back into place until you release the brake and or accelerate; causing this mysterious clunk.
Please go have your motor mounts checked. This has had an amazing effect on my vehicle. Not only are all the sounds gone but I have also notices that I have increased, smoother acceleration and the transmission shifts more smoothly.
I hope this post is helpful. Good luck!