What causes body odor under one armpit, very strong odor on left armpithat causes bad body odor under one armpit?

Bacteria. Body odor has to do with the way bacteria on your skin metabolizes sweat. Sometimes eating onions and garlic make it worse also. See your dermatologist to find out what is going on.
Something else? Your question is very vague, and it is difficult to give a specific answer. However, The most concerning problem to exclude, is infection, (bacterial or fungal) as well as possible malignancy. You should see your doctor to begin a workup.