Care for your neoprene water shoes as you would for any neoprene wetsuit.
You can use any search engine and search for 'wetsuit soap' or 'wetsuit wash' and will find suitable products. Stop by any dive shop where you are travelling and they will likely have some.
If you are using them every day, you probably should not be storing them in a plastic bag. You should be washing them in fresh water (warm or cold, not hot) with cleaners/soaps designed for use with neoprene wetsuits. In a pinch, a mild tearless baby shampoo can be used. Washing them thoroughly, rinsing them well, and hanging them to dry in a well ventilated place is appropriate. You do not want to dry them in direct sunlight as it will over time break down neoprene. Ventilation and circulating air are the key factors.
Storing wet neoprene that has not been effectively cleaned, especially in a plastic bag, will only encourage bacterial growth which contributes to bad odors. Additionally, I would say do not use newspaper or paper towels stuffed inside them, as this impedes air flow and the damp paper will only serve to confine moisture inside the shoes. You're better off washing, rinsing, hanging, and letting air circulate through/around them. If you can turn them inside out, this will also help them dry more thoroughly. In a hotel, a few minutes with a hair dryer on a low setting and held about two feet away will help--but be careful, you do not want to heat the neoprene, just simulate the equivalent of a warm breeze flowing.
If you are wearing them every day, and even after taking them off considerable time passes before you can wash and rinse them, you should be checking to see if they are in fact drying 100% overnight or if they are still slightly damp when you use them the next time. If this is the case, you have insufficient airflow and too little time. A fan helps. A better solution might be to buy a second pair, and wear one, while allowing the other a full day or two to dry before their next use. If it will be any length of time between wearing the shoes and being able to wash/rinse them, clip them to a pack or your waist/belt (using a snaplink, D-ring or spare bootlace/shoestring) and let them air dry as you walk. If you finish crossing the last fresh water river or stream near for the day, rinse them in that water, before clipping them to your pack/waist and moving on. Keep in mind that even freshwater streams/rivers will have bacteria.
If you're unable carry them outside your pack/person then a good wash/rinse at the end of any day's use and ensuring they have plenty of airflow/ventilation is all you can really do. Just make sure you have them out drying whenever possible.
Another possible solution/option is to get non-neoprene water shoes that have mesh uppers, or some sport/water sandals so that the neoprene is not an issue. I make use of sport sandals with a closed toe for uses where there will be frequent immersion in water and wear my neoprene shoes or boots usually for short term activities, like diving or a cold weather kayak trip. It's just easier for bacteria to hide in neoprene and it will be an ongoing struggle against odors with daily/prolonged use.