Say no to gasoline, kerosene, vinegar... even if these methods really help. It's not worth it. Think about the stink that you get as a bonus.
It's better to try and stop using regular soap, washing powder and soda. The result is unpredictable and there are lots of scary stories about sneakers being screwed up this way. The only thing that the sneaker specialists and our grannies agree on is that nail polish remover is still the best way to bring back the whiteness of a light colored sole for a minimal price.