Toxicity of salt depends on contact time. 50 g NaCl per liter kills nearly all bacteria in 2 days. 100 g NaCl/L may do a quite thorough job in 30 minutes.
Body odor is caused by bacteria that feed on the fluids produced by the apocrine glands, mainly present under the arm pits and other areas with abundant hair follicles. Bacteria in the skin feed on the products of the apocrine glands and convert it into odorous compounds. Skin microfauna includes Staphylococcus, Micrococcus, Corynebacterium, Dermabacter and others. As pointed out by others in the comments, treating your cloths against bacterial growth may not be the most efficient approach, as the bacteria are residents of the skin. Nonetheless, the following studies addressed the antimicrobial effects of salt.
A study using the gut bacterium E.coli showed that survival in 5% NaCl (50 g NaCl per liter H2O) was <0.01%. In 2% NaCl survival survival was 8%. The contact time was 48 hours (Carlucci and Pramer, 1958).
Another study examined the effects of salinity on E. coli using a shorter contact time of 30 minutes, and concluded that 10% salinity killed 80% of organisms (Somani et al., 2011).
Sea water, which has a salinity of about 3.5% contains low numbers of bacteria (Carlucci and Pramer, 1958), suggestive of toxic concentrations of NaCl, the major salty constituent in sea water.
Although E. coli has been associated with skin fauna and body odor, I must note that Gram negative gut bacteria as used in the two studies above may not be representative of the mainly Gram positive microfauna found on the skin (Strauss & Kligman, 1956).
- Carlucci and Pramer, Am Soc Microbiol (1958)
- Somani et al., J Eng Res Studies (2011): 40-43
- Strauss & Kligman, J Invest Dermatol (1956); 27: 67–71