I've heard of a good, cheap method of killing all the fleas in one room, but I haven't tested it because I've never had fleas.
1. Cover or black out the windows in the room and turn off the heating.
2. Place a tall, thin candle in a large (wide and shallow) dish or container of water.
3. Light the candle, turn off the lights, then close and seal the door. Leave for 24 hours.
The theory is that as the dark room becomes colder at night, the fleas will gravitate towards the only heat (and light) source i.e. the candle, but because the candle is in water they'll drown as they land near it.
Like I said, I've never tested it myself, but it's worth a punt and should only cost you one candle and a roll of tape (and because the candle is in water, even if a fat flea somehow managed to knock it over, it's unlikely that it would cause a fire).
However, this doesn't address the cause of the problem which are probably the cats, so you should treat them with some kind of anti-flea treatment otherwise the fleas will just come back.