When I put my car into Drive, the car makes a very loud clunk noise as its going into gear, it the original automatic 1993 ford tempo transmission, it also does the same thing going into reverse, not everytime, but quite often

Sounds like a bad U joint in the drive shaft or axle CV.joint .
When you go over a bump or hole the wheels move up and down the drive shafts and axles have to move along with them or they would bind and break something in the drive train .
When they ware they tend to clunk going in gear power on they get tight power off there loose that's why it makes a noise .

check ur cv axles one may be going bad also check steering and suspension system--struts worn, loose --ball joints goin --even tie rods can cause play

Mine was the centrebearing which in turn failed broke the rubber coupling at the gearbox side and snapped the tailshaft so be careful driving

If this is an older rear wheel drive vehicle you should have the "U" joints checked is the drive shaft as one may be going bad.

sounds like the universal joints on the rear drive shaft

if the whirring you describe sounds like an airplane and increases with speed that would be a wheelbearing and it may be loose to cause the clunk noise. when it is put in 4 wheel drive that can load the bearing up and noise goes away.

Sounds to Me Like There is a "U" Joint Problem Here. Although normally it would "Clunk" upon Engaging Forward or Reverse, I would RULE OUT This FIRST, Then move on to Motor Mounts, Transmission Mount, Then DIFFERENTUAL= Pinion Bearing ETC.
PLEASE DO NOT Count me OUT, as I am Available to Answer Questions as you go along with your Inspection, ALONG with MANY MANY Other GURU's At FixYa.com . Good Luck With Your Search & Hope you find its's a Small Problem.

Three probable issues;
1-The transfer case is low or out of fluid.
2-The drive shaft may be out of alignment due to worn front or back U joints (thus the clunk on shift)
3-the shift lever is out of alignment with the shift mechanism on the transmission housing.

Make turn left noise will be on right, turn right noise will be on left this is CV joints.Make donuts.

My 2003 F150 Supercrew would not engage in 4x4, it ended up being the shifting fork in the front end, cost me $200.