Although perspiration or sweating is odorless when mixed with bacteria, it often causes an unpleasant odor. Other than body odor, garlic side effects include bad breath, diarrhea, stomach pain, heartburn, nausea and gas. Sweating and body odor is treatable and preventable with lifestyle and dietary changes. Medication may be required to help treat sweating. Allergic reactions and asthma may occur as a result of garlic, consult a doctor if you experience moderate to severe side effects.
Garlic is a strong herb with a chemical called allicin. The sulphur compound chemical when broken down gives garlic its strong smell by creating gas compounds. Allicin seems to help treat heart and blood related conditions according to National Institute of Health, Medline Plus. 
Cause of Garlic Sweat Odor
The apocrine glands grow in the hairy regions of the body such as the scalp, armpits and groin. This is where fatty sweat builds in the tubule glands according to Mayoclinic.com. When garlic metabolizes it releases a gas called allyl methyl sulfide or AMS, which absorbs into the blood. AMS travels to the skin where it excretes with fatty sweat in the apocrine glands causing a garlic odor. The garlic odor may persist for several days through sweat and breath. 
Treatment of Garlic Odor
A sure way to prevent a garlic odor is avoiding food with the herb. However, authors of "Journal of Food Science," published in 2010 reports that milk can neutralize the odor produced from garlic. The journal reports mixing full-fat milk with garlic before ingestion is the most effective method. Milk contains a compound that counters the AMS gas. The result of the study suggest any food with high water and fat content may help reduce the odor and taste of garlic. 
Allicin is an unstable chemical and it changes quickly. Ageing garlic makes it odorless due to the low amount of allicin, reduced from ageing. Medline Plus says ageing garlic compromises its health benefits. Aged garlic is available as a supplement.