Do NOT put chlorox on any living thing; hamsters have very sensitive skin and respritory systems. Rodents in general are hypersensitive to all cleansers; most places I've worked will not even mop the floor with dilute bleach of the rodent is in the same room.
Please take your hamster to a vet; severe parasite infestations can lead to devastating anemia (well, providing they are the blood sucking type), as well as secondary infections from scratching. Your vet can perscribe something (probably ivermectin) to get rid of the parasite infestation. In the mean time, you can keep his cage very clean, keep him well fed and watered, and give him a warm bath here and there to rinse off loosely clinging mites.
Good luck!