The most likely cause of the brake noise is the dust shields rubbing against the rotors. The rear ones are especially bad for that. If simply bending them away from the rotor doesn't prevent them from touching, then rip them off completely. They are usually so rusted that they've lost all their strength. You'll notice that the "heatshield" part is much thinner metal than the "backing plate" part that the park brake shoes are attached to. Leave the backing plate on. P.S. New ones are like $150 each...really not necessary. I have 5 Avalons...4 have the heatshield removed!
If that doesn't solve the noise issue, then pull the caliper and pads, rotate the rotor and listen if the parking brake assembly is the culprit. Sometimes the brake shoe mounting hardware rusts/breaks or was incorrectly installed. Check out my youtube video https://www.youtube.com/watch?v=S_mg_C14ySI
Note the tabs on the spring washers that retain the shoes (@8:50 minute mark). Also notice the if spacer bar is installed correctly.
As far as the original question in your post: Did you install complete "QuickStruts" that included new springs, etc OR did you change over your old springs onto new struts? I would begin by checking the upper mount bolts (the 3 behind the seat cushion) to make sure they are coming loose. If you did re-use the old springs, it is easy to mis-align the rubber isolator that goes between the spring and the strut. It could also be the top cap out of position or worn out. Good luck.
I had a 98 Avalon with a clunking sound. The problem was on the front right side, it turned out to be the sway-bar link bushing had disintegrated. The hose from the reservoir to the power steering pump was leaking fluid onto the sway-bar bushing, I repaired the leaking hose and replaced the bushing and all was good!
Further research I found out that rubber and Petroleum based products don't play well together, I recommend using Silicon based lubricants on rubber bushings.
That's my 2 Cents, for what it's worth! Good Luck, You're definitely in the right place to get some good advice.
98 Avalon 485,000 miles Sold, it was still going strong
01 Avalon 242,000 miles (daily driver)
So, as expected... I didn't install the adjustable end links correctly. Last time, the issue was the bushings, and now this time, I didn't install the adjustable end links correctly. YOU HAVE TO GET RID OF THE PRELOAD OR YOU WILL BREAK YOUR END LINKS. Since they are adjustable, you have to get rid of the preload because it's very easy to have both end links not properly even or one side could have preload. I then jacked up the car and found that the end link was popped off of its thread where you twist and adjust it. The end link was loose and was not properly installed with TONS of preload onto it I'm assuming.
I simply fixed this issue by unbolting both end links at the bottom end where they connect to the rear sway bar, then slapped the wheels back on and dropped the car onto its tires so the end links are dangling and loose and not yet connected to the swaybar. Then I drove back and fourth to get the suspension settled just in case it had preload. Once I did that a few times, I then jacked the car up and only put ONE end link bolted to the swaybar then dropped the car again. Now that one side has the proper length, now it's time to get rid of the preload off of the rear swaybar.
I then dropped the car again so the one side had a fully bolted on end link, and the other side had the bottom end unbolted... then I got under the car (WHILE THE CAR IS ON THE GROUND AND THE FULL WEIGHT OF THE CAR IS ON THE SUSPENSION.) I then took the other end link and adjusted it where you can slide it through easily without resistance. It's a true pain in the ass and tight getting under the car while it's on the ground if you don't have car ramps or a lift, but you just have to keep adjusting until the final end link can slide freely through the end link hole and then bolt very tight and you are done!
Did a quick test by pushing down hard on the rear of the car, no more clunk or squeaking from the rear end. CLUNKING NOISE IS NOW GONE WHILE DRIVING AS WELL AND HANDLES SO AMAZING!
Now, I do have to say the adjustable end links are so much more work, but it's so much more worth it. Plus it compliments the performance Whiteline BTR39 20mm sway bar kit that I have installed. The stock sway bar is 16mm and the Whiteline is 20mm so a 4mm in difference IT HANDLES LIKE A DREAM!!!!!!! AND I DON'T EVEN HAVE COILOVERS. The car takes corners so much better and body roll is reduced drastically. BEST DOLLAR FOR DOLLAR MOD MONEY CAN BUY HANDS DOWN! The car feels more fine tuned so I'm a happy guy!
Now, as for the brake issue with the squeaking professor sir was absolutely correct. The heat shield was bent towards the rotors and was causing rubbing and squeaking. So, I just ripped it off completely Oops :p .... The heat shield on these cars really get in the way over time, I had to rip off the other heat shield on one occasion because it literally just fell off and it was rattling so loud.
Anyways, thank you so much for everyones support on finding the solution, glad you guys are here to help when needed.