How to remove deodorant/sweat stains from black shirts?

Mix 6 ounces vinegar and 1 ounce of good, liquid, laundry detergent (Tide, Wisk, Era, etc.) and apply the mixture to the stained area. Soak the stained area good & rub it in with your fingers, both sides, for 30 seconds . Do NOT use a brush, as it will discolor the fabric.  Wait 15 minutes and rub for 30 seconds again. Do this 4-5 times, keep the area soaked. Spread the shirt(s) on a non-porous surface, making sure the 'pit' area is soaked, place an upside down dinner plate over the area, to keep evaporation at bay, and leave it overnight. Rub the area the next day, and wash with the warmest temperature the fabric(s) allows.

To prevent these stains from happening in the future, switch from using an antiperspirant deodorant, to a regular deodorant. 

Most antiperspirant deodorants use an aluminum by-product to keep sweat at bay, and this substance rubs off on the under arm of your shirts, causing those stains.

I don't think it is from the deodorant. I think it is from your sweat. Try using baking soda instead of deodorant 

Very difficult to shift. Try wetting the shirts  and working a paste of biological washing powder into the area then leave at least overnight. Then wash as normal. Might not work, but a few tries will at least mitigate the situation.

I usually spray it with water and stick an iron up to my armpit.

Dab on vinegar, then immediately wash it.