I have discovered the best kept secret for eliminating underarm odor. It is organic virgin coconut oil. I cook with it as well because it is very nutritious. I have always needed a strong anti-perspirant, but no more.
This page contains the following solutions.
Underarm sweat only smells because of the bacteria that grows there. If you use an antibacterial soap (I use one called Safeguard), you won't need to apply deodorant as well.
Underarm odor (aka Bromhidrosis and Erythrasma) is caused by a bacteria that adheres to your hair follicles and skin and when the (odorless) sweat comes into contact with the bacteria on your armpits, the odor begins! Ewww!
Armpit odor is not only embarrassing but may be difficult to get under control. This is a page about remedies for armpit odor.