A4WD is not AWD
First of all, the Expedition does not have All Wheel Drive. It has 4 modes: Rear Wheel Drive, A4WD (Not AWD) which is Automatic 4 Wheel Drive, 4 Wheel Drive Hi range & 4 Wheel Drive Low range.
A4WD works like a limited slip differential, when the sensors detect rear wheel spin it engages the front differential making it 4 wheel drive.
Secondly, 4 wheel drive should not be engaged on pavement, wet or dry. It should only be used on loose gravel, heavy snow, mud and other such surfaces. On pavement there is not enough slip between the tires & surface which causes the drive components to bind up, when they do, something has to give, if it's the tires scraping or hopping you're lucky but if not the drive shafts, yokes, U-Joints, transfer case are all under stress, when it pops, you'll know it.
On dry/wet pavement & puddles you should use 2 Wheel drive, on light snow (or wet, if you like) you should use the A4WD.
If you want to see about that binding I mentioned, go into a parking lot, engage 4WD, turn the wheels fully left or right, put into drive (or reverse), and take your foot off the brake slowly. Let it roll slowly, it will come to a stop by itself very shortly. This is what your car is trying to do when you're incorrectly using 4WD on the roadway. The reason is because the wheels & axles are turning at slightly different speeds, which causes the binding of the drive-line.
AWD that some vehicles like Mercedes, Subaru etc have uses a transfer case that allows slippage between the front & rear differentials actual 4WD does not. So called Full Time 4 wheel drive is basically AWD.
Some of the older Expy's don't have the 2WD position, so for most driving, you'll use the A4WD mode which will run as rear wheel drive till needed.
All tires should be the same size (un less you pull the 4WD fuse or you have 2WD mode), if not the sensors see the difference in speed as wheel slip.