It's been theorized since baking soda reduces acid (more of an acid/alkaline balance), it also might help reduce odors. As for vinegar, it's suppose to be kind of an Antibiotic I think? It also might help against h. pylori, the bacteria that live in our stomaches since it's a lot like stomach acid and h. pylori neutralizes stomach acid to survive.
Wish I could help you more but I've taken both vinegar and baking soda off and on for my heartburn and haven't noticed a reduction in odor.