I feed my dog raw, chopped garlic daily and though we live in location where fleas are abundant I have not found a flea on her in two years. I started when she was 5 weeks old.
I now give raw garlic daily to a kitten who is almost 6 weeks old. I started when he was 3 weeks old or so. For the kitten I mash the garlic in a mortar then add water. So it is really garlic juice he is getting mixed in with his wet food.
I check him daily and so far the fleas seem to have fled.
Fleas WILL NOT cross or live around Sulfur, FACT! The fleas eggs hatch on 10 day cycles, FACT! Boraxo Laundry Power WILL dry up flea eggs, and they WILL NOT HATCH!
None of these things bother the animals, and a vacuum cleaner WILL get them up!
Make a small pen outside and super saturate the floor with sulfur, and put the animal in hold up for 30 mins after being outside!
But first solve the inside problem!
DO NOT use tea tree shampoo on your cat as someone else suggested. Tea tree oil is POISON to cats.
Bath your cat every day with, medical shampoo like t-tree and them wash them after that with hibiscrub to stop infection. Should work a treat