Okay, my suggestion; as I've seen topic related to this, and I always check in to see if there is something a little easier than, what I'm currently doing to prevent excessive armpit sweat and odor. Unfortunately, I always hear the same thing...
Now before attempting this, please check with your doctor, to make sure you do not have thyroid problems. Usually that is one of the LEADING causes of armpit sweating. Followed by odor.
Here is the method I use, and you all will probably find it crazy. But it REALLY works. I have botox done under my armpits, once a year. Please take note this does not cure the problem. It stops the problem, for a year though.
Botox under the armpits is semi painful, but for someone like me, who sweats A LOT. I'll live with the pain. I can wear grey shirts, and wont see the stain of sweat. And odor?-- NONE!
This costs me around 1500 a year to maintain, but seriously, seek medical opinions before doing this. It may work for me, but I went to my doctor, and consulted him MANY times over, before taking this route. :)