If it's really that bad, I'd get a gallon bottle of Clorox Bleach and pour it down the drain. Then run water to fill the grey tank completely. Let it sit for a few minutes then drain it! If bleach won't kill the smell, then you must have a dead animal decomposing inside the tank or something.
I don't understand why your P-traps would not work. If you have water in them, they should prevent smells from coming up. Check under your sinks and make sure you have one of these on the end of a pipe (Anti Siphon Trap). If you do, it's bad (or broken) and letting the smells pass through it.
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That fact you have those kinds of smells coming from the grey tank at all, tells me the previous owner left his tank drain valves open all the time. Water ran out, but food particles from washing dishes and such did not. Now there is a build up of food particles decaying, rotting, causing the smell.
If the bleach does not rid the smell, (considering you cannot move the camper), then get a box of Rid-X or a drain opener with algie eaters and pour it into the tank and let it sit for a few days before dumping. The bacteria eaters will eat up and soften any food build up off the inside of the tank and will finally flush down. But it takes a few days for the emzines to eat themselves out of food.