I saw the title and thought, "Food odours" aren't dangerous, because what do Brits or Kiwis have to deal with, anyway? Crazed stoats and prickly hedgehogs in the UK? Introduced oppossums and flightless birds down under? But, seeing as you're now wondering about food odors in North America - yeah, good to think about.
Don't use detergent on coated fabrics. One of the ways detergents clean is because their low surface energy allow them to slip in between dirt and the fabric. Alas, they can also get between the fabric and a coating, causing it to delaminate. Use a soap (Ivory, Dreft, etc) rather than a detergent (Tide) if you are going to launder anything. Better yet, get a down-specific or Goretex-specific soap from REI, etc.
And on using white gasoline to remove odors: Yes, it will work very well to dissolve many smelly, oily compounds that water won't dissolve. And nylon is resistent to gasoline as is high-density polyeythlene (HPDE). But gasoline (white, mo-gas, or av-gas) can soften low-DPE. And polypropylene is very oilaphilic - that's why it hangs onto body odors. And coatings? I've never thought to risk it - seems likely to go badly.
Start with mild soap in warm water. Escalate only if needed.