Get Your Cat Care Questions Answered By Cat Vets ASAP
Yes a solutoin of bleach does kill giardia particularly if it is left on the surface for at least a minute before being rinsed off. One part bleach to 30 or 32 parts water should work.
You would want to clean the cat boxes with bleach (and rinse well after) and totally change the litter.
You can clean the scratching posts and carpet and rope on the cat trees with the bleach solution in a spray bottle (just wear clothes that you won't be sad about if they get some bleach on them). Some people feel steam cleaning carpets is helpful.
You might ask the vet to bath the cats so they can't reinfect by washing themselves.
You can read about giardia and the oocyts and survival time etc here
If you have a well, and you don't drink the tap water, but the cats do, then you may want to get your well water tested.
Hope this helps you!
You might do steam cleaning of the upholstered furniture or use one of the cleaners for them, but if the house is dry that can help kill the oocysts too.
Yes the cats can leave oocysts and other health hazards like e.coli on counters from walking on them, particularly if they have just been in the cat box. If the cats are up on food prep surfaces you really ought to clean those surfaces pretty regularly.
I'd wash and disinfect any food and water bowls too. You might as well minimize chances of reinfection while the cats are at the vets.