I live most of the year (10-11 months) in Latin cities where the humidity is high and the temperature is frequently 40 C. My husband of the last 8 years and I have discovered several things that help keep natural (and the way funky unnatural) body odor bacteria at bay.
1. We manscape our pubes and armpits. We don't shave off everything. We just keep "enough" pubic hair neatly trimmed. The less hair, the less play and breeding ground for the bacteria that generate funky stank.
2. We use plain glycerine soap scented with lemon peel oil to shower and bathe. It's cheap and doesn't dry out our skin. The same glycerine soaps (there are hundreds of manufacturers all over the world) also scent the glycerine with orange peel, lavender, lemon grass, rose petals, lilac -- you get the idea. But for the last several years the lemon smell is the one I prefer and that also lasts for a few hours after showering.
3. We do use deodorants upon occasion, but not every day. Instead, we each have our own deodorant salt crystal sticks (every health and beauty store carries them) for hitting the armpits and sliding between our moistened thighs. Note: We never use each other's stuff.
4. Because it's usually so hot and humid we tend to shower a minimum of twice a day, if not three times a day. To avoid dry skin I use cocoa butter (looks like a regular Hershey chocolate bar, but when you open it is just creamy white cocoa butter). The Husband uses expensive exfoliants for his face and expensive men's body creams. He's still stuck in the Hugo Boss era. But he never crawls into bed smelling like Hugo Boss products. He'd get the same moisturizing effect from some unscented body lotion, but . . . well, he's Argentine and porteños are BIG on splashing on lots of perfume or cologne. I, on the other hand, like smelling like chocolate.
5. As for what I refer to as the famous 'Mericuhn Butt Odor, we have bidets. So, in addition to the first phase of wiping one's ass with toilet paper we follow up (as do most people in Europe and large South American cities) with a comfortable warm soapy butt wash and a dry off with towels kept handy specifically for that purpose.
Unless you've been eating lots of garlic and live in a country where garlic is not commonly used in the local cuisine, you shouldn't have too much of a problem. Being soaked with sweat after a good run or just walking home 10 blocks from the nearest Metro Station is a great thing for your skin. Saunas are equally good. Just be sure to take a good shower and change clothes before getting back on the street (work) or expecting your mate to have no qualms about licking every nook and cranny of your body.
Good luck.
Addition: And two things ManlyBanisters and Vince mentioned are quite true. First, the "Pit Rock" is a salt that creates a Ph environment that bacteria doesn't like and has a hard time flourishing in. The antibacterial scrub mentioned by Vince also works. But in both cases it means always putting clean clothes on and not wearing the same T-shirt and shorts for a week without washing them. You also need to avoid the old habit of smelling a previously worn shirt and risk wearing it once again, unless you're French. Once, while camping for two weeks in the northern deserts of Mexico, I noticed I was beginning to smell funky. The deodorant crystal wasn't working because I hadn't had the opportunity to bathe for a few days (no water). However, imagine my joy when I discovered that rubbing generous gobs of Neosporin or triple antibacterial cream in my pits worked miracles. These are the same antibiotic gels/creams/greases meant for treating open wounds. But don't depend upon them forever. The bacteria are good at becoming immune to the stuff.