Straightening a differential housing is easier than you think, and the most precise tools you could use for this job are already in your head. Your own two eyes. While an expensive laser alignment fixture would be more accurate, it would be by much. The human eyes is incredibly sensitive if provided the right reference points to judge by. However, the eye is also easily fooled by illusions, so care must be observed not to allow that to happen. Below is a procedure proven time and time again to be reliable, fast, easy and accurate. But be sure to follow the procedure close, since success is in accuracy, nothing can be left out or overlooked.

First thing is to completely disassemble the entire axle housing. The gears and differential can stay in, however, it would be better if they we not. This can be done with the axle either in the vehicle or out, however, we are illustrating this with the axle removed.

Now take a 40w-60w light bulb and screw it into an open receptacle… meaning no shroud or cover, just the bulb out in the open.

Butt the bulb up against one end of the axle tube hole, almost as if you were attempting to squeeze the bulb into the hold. Use tape or cord to hold the bulb in place.

Hold your eye about 2 feet way from the opposite hole and look into the tube. By aligning the tube up like a scope on a rifle, use the light emitted by the bulb to line up all the concentric rings it produces along the length of the tube. Note in the photo to the right that the light rings on the closer tube half are perfectly circular, meaning we have the camera perfectly in line.
(yellow) The (red) arrow is the pumpkin opening, and  the (orange) is the other end of the axle tube opening.

Now make note of the far side of the tube where the light bulb is. You can see the axle roller bearing visible, and obvoiusly not centered (yellow). We later measured this with electronic laser equipment which showed this bend in the housing to be less than 1/8", which would never be noticed with the axle installed in the vehicle. This proves just how deadly accurate this simple method can be.

Even though we would have otherwise never event known about this, this slight bend can cause eventual axle failure when using tight fitting splined axles and differential combinations. This is but to the axle being forced to flex as it rotates, kind of like a piece of wire being slightly bent back and forth. While the diagnosis is quick and simple, so is the fix illustrated below.

Take a chain and wrap it around one end as far out as you can get it, and then tie it to the other end. Then insert a bottle jack in to create the look of a bow and arrow such As illustrated to the left.

With the light fixture still installed, carefully and slowly pump the jack to take all the tension up in the chains. As you pump the jack, the tubes will bend in the way you have the jack situated corresponding to exactly the opposite of the bend you wish to remove. Use a block of wood if necessary to protect the housing, and above all, be very careful when working with pressurized tools in this case.

Be aware that very little force is need to bend even the strongest tubes using this method, however, the tubes will want to spring back significantly, requiring a certain amount of over bend to achieve the desired results you are trying to obtain. One trick is to pump up a bit, allow the jack to relax and view the status through the lighted tube. Then go back and give it one extra pump, and look. Continue this until satisfactory results are achieved. It won't take much or very long to complete this procedure.

If you need to bend one tube side more than the other, simply slip the chain a bit closer to the center of the axle on the side in which you want LESS tube movement.

If for some reason you go too far, simply re-position the bottle jack in a new location to bend the tube back to another direction. It won't be difficult to set the tube straight within a few thousandths of an inch with just your eye. The fully repaired axle tube on the right was checked with laser equipment and it was within .013" from being perfect. That less than 1/64th of an inch!!!