Sometimes we only need to use these things for a short while and would have some laundry soap, shampoo and dish soap on hand. However, in the event that you are in a long term sustainable situation you may need some other options.
There are some products that will last awhile that you could stock up on such as SOAP NUTS. Soap Nuts are from a plant that has a high Saponin content. This product can be used for all your soap needs. If you are adventurous, you can research plants in your area for ones that have a high saponin content. In our area the Mock Orange was once used for soap.
Now lets talk about the 'old' options.
Lye Soap - This is something that can be made and was the original soap.
Here are some links for instructions on making Lye Soap: About-How to Make Lye,
Castile Soap- Now that you have some lye soap, you can make castile soap which will be more gentle on your skin, hair and clothes. Here is a link for making your own castile soap: http://www.wikihow.com/Make-Liquid-Castile-Soap
I will add more when I find some others than are easy to follow.
Boiling Water -You can also pour boiling water over your clothes and dishes.
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