I use a veterinary sanitiser for mine, but a trip to the chemist/pharmacy should get you a good antibacterial like hibiscrub (the stuff they use in hospitals) to spray on it. Bleach is too strong for plastic parts and if you get a spray you can ensure any uneven surfaces (like on polystyrene) are reached. Dismantle what you can to get the fluff out of a fan if you have one, mine gets full of it. Sun dry if there is any sun! Best steriliser going. Ultra violet lights kills so many nasties.
As mentioned before hatching does have it's own distinctive smell, as do day olds, but it shouldn't make you want to gag unless you have an extremely sensitive nose! The smell is from bacteria's excretions, gases and fluids from them. You can't stop them getting in to your incubator during incubation, they are in the air, the breath you breathe over them, your hands, the water you add to the incy, everything. Best you can do is give the eggs a good start by keeping your incubator immaculate bot before you start and after a hatch!
As for rotten eggs, I have never had one, or a popper as I candle mine religiously, but I have not heard of anything that will get rid of that smell if one blows. Maybe baking soda and weak lemon juice/water solution before the antibacterial solution?