Cleaning
Dust is the usual enemy. A soft brush gets it out of the crevices without scratching the varnish.
Sticky or greasy
Warm water with a drop of washing-up liquid, a soft toothbrush, then let it air dry on a paper towel. Do not use alcohol on a varnished monster: it clouds the finish.
Moss Mon
Moss Mon is flocked. Do not wash him. Blow the dust off, or use a hair dryer on cold.
Lantern Imp
Cleaning does not affect the glow. If the glow fades after a year or two, that is the pigment ageing, not dirt.