I would use bleach personally. Just dilute according to the instructions on the bottle, soak, rinse really well, and if you are still concerned you can put everything in the sun for a few hours and let it evaporate.
If the gravel is porous then you can't use bleach on it and I would recommend replacing it altogether. Everything else should be fine though.
Sorry about your boy :( It's always hard to loose a pet. As an aside, what kind of mug is it? Some pottery can leach chemical into the water, which actually happened to me once. Luckily I noticed the change in my betta's behavior very quickly and was able to remove it ASAP. So, just a word of warning that I like to pass on to others.