Here's what I learned from Martha Stewart.
The purpose of a soap is to cut the surface of the water. This allows the water to go through the fabric to clean it. So any soap will do. I use...get this... dish detergent. It has less fillers, which detergent companies use to add weight and make you pay more (it's usually crushed stuff that has nothing to do with cleaning at all!) and does the same thing.
For freshness and to get rid of odor, especially kid and cat odors, I asked for the help of my day care provider some years ago. She suggested something I never thought of, ammonia. It works WONDERS! Absolutely gets rid of odors, even though it has an odor of it's own!
For the dryer you can use a liquid rinse agent in a washcloth. You can use the same washcloth over and over and it's much cheaper than the sheets. On vacation I do carry the sheets, though.
HTH!