1997 Ford Explorer AWD Problem

check for bulges in the side walls of the tyres and check for belt separation. Disconnect the front axles into free wheel mode and if the noise is not there it will be tyre related as there is no movement in the diff or drive axles

Sounds like you have either ball joint issues, or problems with the CV joints. The other possibility is a problem in the transfer case causing the front axle to bind. You can physically look at the CV joint boots to see if they are torn open and many times you can grab onto the axle and give it a good tug to see if it will move..it should not.

Sounds like a transfer-case problem. It could be an internal gear problem or shift fork binding up or even a broken chain which all require it to be opened up. If it is the electronic version it could be a bad solenoid or loose plug connection.

have the "U" joints or cv joints checked at the front end

Bearings in the transfer case have failed and causing gear damage, replace the transfer case.

just had one diagnosed to being the aft coupler on the front driveshaft where it inserts into the transfer case. It only does it when under power, correct, and once in a while durring coast down.

You have to take the rear differential apart, and then pull the axle.

I would check out the hubs and the drive axles first before changing the transfer case but I would do a differential service also if you never had it done since you have owned the car a 91 aerostar that is all wheel drive I thought I had the same problem and I replaced both hubs and one drive axle

I have the same problem with my 94 explorer with a manual transmission, Just replaced the trans a month ago because of gear failure and now It's slipping out of gear when the engine isn't under load aka Coasting, was Told By a Really good Trans Guy that this is a failure in the Linkage in the transfer case am about to tear into mine tho It's way over my technical ability but will repost here after I get it torn apart with potential prices for worn parts for the do it yourselfer, And Has to be the issue I hope because the gears in the transmission are in pristine condition the other reason for suspecting the transfer case is that when my trans is slipping and making that weird Rattle Clatter sound coming from the trans if I put it in 4x4 low it drives great even tho the front wheels aren't pulling since I have the front drive shaft off at the moment,, Well Here goes Nothing Wish me luck on this teardown gonna need it..

is your universal joints out and that is where its rubbing?
running different size tires on a all wheel drive is a big mistake it can burn out the transfercase