You probably have some organic material anaerobicly decomposing, residual food stuffs probably.
Depending on total capacity, and how full it is, a quantity of bleach (preferably in a sinkfull about to be drained) down the sluice should silence your noxious microbes.
Pre-rinse and scrape before doing dishes. A mesh drain trap is good too, to catch all of that large stuff that won't easily drain out, and later morphs into odiferous gunk...
Can't help you if you want your grey tank smelling minty fresh!
Those who say that it cannot be done should not interrupt the people doing it.