In these times, when using soap for handwashing is extremely important to help preventing the spreading of diseases like caused by COVID-19, it is helpful to have knowledge of making soap, even at household level. Plant oil is a major ingredient of soap, the other is lye.
Almost any oil can be used to make soap, in practice most oils used are: olive- and palm-oil, coconut-, sunflower-, groundnut-, but also oils from neem, jatropha, castor, moringa, etc
A Forum on Soap making can be found at : https://www.soapmakingforum.com/
It has a rather complete overview of all possible oils used to make soap, plus a calculation tool for determining the right ratio of the ingredients, like oil, water, lye and eventual additives for smell or colour.
Another source in which receipts for making soap at house hold level are described is the Smart-Hygiene-Solutions booklet, see: http://smartcentregroup.com/wp-content/uploads/2020/05/Smart-Hygiene-Solutions_V2.1_04MAY2020_LQ.pdf .
One of the simplest recipes for rural households referred to is making soap from grinded seeds, like Jatropha seeds, see the FACT Jatropha Handbook, Annex Page D5 on this site: https://www.bioenergyforumfact.org/reports/fact-jatropha-handbook .
No oil is required then, the only ingredients are oil containing seeds, potash and water.
Seeds from Castor, Palm, Neem, Jatropha, and Shea Nuts are being used to make soap in this way, but probably many more seed types will be used.
Potash (Potassium ash) can be made from ash of hardwood or plants that contain potassium like banana peels, cacao pods, tamarind pods, etc. Plants are dried, roasted and ground into a powder. Recipes for making lye using potash and water are given in both documents from the links mentioned above.