Fleas are the worst.
The first thing you should use is Capstar on them. They are ingestible tablets that make your cats blood toxic to fleas, but it runs through their system in a day. So it only kills adult fleas on their body.
On the day you give them Capstar, get flea carpet powder and follow the directions & vaccum it up (if you have carpeting, that is.) You also need to wash any material your cats sleep on frequently (they will have laid eggs in those areas.)
Then the following day, put Advantage on them. The fleas that were still larvae when the Capstar was working to kill off the fleas will eventually hatch and the Advantage will kill them (Advantage is the stuff you put on the back of their necks, it lasts about three weeks.)
And no, using both Capstar and Advantage won't "overdose" your cats, the pesticides operate in different ways.
Most "flea dip" is just a normal shampoo with heavier surfactant content and some weak ass pyrethrin pesticide in it. It's probably no more effective than dishsoap, which will help drown a few adults and loosen some eggs off of their fur.
Whatever you do, don't use Hartz cat flea liquid. It uses an incredibly harsh and not very effective pesticide. Some cats develop nausea and vomiting, seizures and some even die from it (you can find horror stories all over the internet.)
Also, never use essential oils. There's some dummies on the internet who just say to put tea tree oil on your cat to kill fleas.. But it's not good for your cats organs.
Stay strong, fleas are an absolute menace and won't go down without a fight and expensive flea treatment.