If you've had a cat then yes the fleas could have come from that into the house or feed off humans or other animals. Not everything on the internet is expert in hamsters though. Have a linked a site below that is a reputable information on Hamsters and it gives some detail about different types of fleas and what to do about it. Seems that general house cleaning regularly should solve it fairly quickly. However if some of them are possibly biting your hamster I would suggest taking him to the vet in a pet carrier (or small cage if you don't have a pet carrier) to be examined. They can test for mites at the same time and diagnose whether he has flea bites or not or whether he needs any treatment. Whatever you do don't buy or use any flea treatment or your hamster - it can cause serious health issues and even skin burns or respiratory problems, unless prescribed by a vet. According to this article the fleas are very unlikely to actually be living on the hamster but living nearby and just landing on the hamster to feed.
It sounds like one of those process of elimination situations. The fleas are more likely living in the house and feeding off the humans and possibly your hamster but not living on them. Sounds like a lot of house cleaning and hoovering regularly! Whereas for the hamster you would need a vet check and then probably a full cage clean.
Freezing will kill fleas, eggs and larvae (just checked this as freezing doesn't kill everything!). So you could bag up bedding in smaller bags and freeze it to make sure it is ok before putting it in the cage after the cage clean, and otherwise just wash down the cage and any toys or items. Rough wood items might need to be thrown away.
I think I would tackle it like this:
1) Have a big house clean. Freeze your bag of hamster litter.
2) Have another big house clean a week later. Clean out the hamsters cage - wash everything in warm soapy water and rinse well and dry and replace all the litter with the litter that has been in the freezer. Hide lots of treats in the cage for your hamster to distract from the cage clean!
3) See if everything subsides
4) If your hamster is still scratching, take him to the vet for an examination and skin scraping test. But don't do another big cage clean until you have results.
If your hammy doesn't have any sore places I wouldn't worry too much. Are you sure it's fleas and not just mosquitos at this warm time of year?
Hamsters Fleas