Hello:

I got 'em flying around, but how do you tell what they are, and are they on my cat?

excon

Fleas hop, gnats fly.

You could try a spray bottle with some Olive Oil and add a couple drops of Peppermint or Lavender essential oil.

Adding a dessertspoon of natural apple cider vinegar to the water bowl will make the skin more acidic and unpleasant to fleas and ticks. If your dogs don't fancy apple cider vinegar in the water bowl, dilute it 50/50 with water and use in a spray bottle instead of the citrus repellent. [Or, you can use natural apple cider vinegar tablets.]

Natural Flea Remedies

I am not so sure I would use eucluptus because I have heard it can be toxic to cats but the other stuff should help

Sprinkle the floor with some salt
Sprinkle the yard with seven dust

Hartz, Ritz and Seargant's and other grocery store flea products don't do anything.
Zodiac is a little better than any of them

Frontline is good but expensive.

Put your bananas away...