You are describing a condition called bromhidrosis.
There are some cosmetic procedures that are quite valuable, but I would recommend starting with simple, and far less expensive measures first.
Hygeine in the area such as thoroughly washing the axillary vault (the whole armpit), prompt removal of sweaty clothes, and the use of a deodorant ( rather than antiperspirant). Adherence to a regular shaving routine will minimize the growth of bacteria and sweat on the hair shafts. Electroylsis might help.
An antibacterial soap such as Lever 2000 or even Hibiclens wash will further limit bacteria. I usually prescribe Acanya in this area. It has topical Clinamycin and the Benzoyl Peroxide is only 2 1/2 % which is less irritating than the 5% found in Duac or Benzclin.
If hyperhidrosis ( excessive sweating) is a factor, then an OTC antiperspirant ( Mitchum is a good choice) or an aluminum Chloride product such as Drysol can be used. However, ameloriation of hyperhidrosis does nt reduce apocrine sweat production and it is actually the breakdown of apocrine sweat by bacteria ( forming foul smelling fatty acids) that causes bromhidrosis.
These measures usually work to control mild body odor. If you desire a more permanent treatment, a frequency doubled Q-switched laser is effective. Botox may also help, definitely with the eccrine production and perhaps, slightly with apocrine secretion. This would have to be repeated every 9 months.
Surgery can also be used in recalcitrant cases. However, this leads to scarring and often the bromhidrosis can recur. The apocrine glands are simply removed with the subcutaneous tissue.
Superficial liposuction curettage has also advanced as a therapeutic option. It is less traumatic since a smaller incision is used.