I dilute the vinegar for cleaning the bathroom. An hour later, I can't smell it at all (and I hate the smell of vinegar!). For mirrors, I mix up 1 cup of water, 1 cup of rubbing alcohol, and about a tablespoon or 2 of vinegar. It works much better than plain water.
I saw on Martha Stewart that you can use olive oil and lemon juice to polish your furniture. The lemon gives it a nice smell, and the oil is good for the wood.
If you want a nice smell, try putting a drop or two of essential oils into your mop water. I've never tried it, but I'll bet that would give a nice smell without chemicals.
You might also want to look into making your own laundry detergent. If you google Fels Naptha soap, you can find a pretty easy (15 minutes) recipe that will make enough to wash about 64 loads. It's not totally chemical free, however, but much more natural and WAY cheaper than anything you can buy commercially. I'm experimenting with other ways of making the soap.
As for the dryer, I don't know that I can give you a really good solution. I use dryer sheets occasionally--the free and clear ones. I find that loads only get clingy if I seriously overdry them, or if they have synthetics in them. Cotton has to be VERY dry to get static. Synthetics will stick to each other once they have dried (and they dry faster than cotton, generally), so maybe set the dryer to less dry and take out the synthetics before the cotton is dry. If you iron, you could take things out 95% dry and let them finish air drying, which would eliminate most of the static problem. But I'm sure someone else has a better solution. I use very little synthetic, so it's usually not a problem.
Hope that helps!