I am trying to make so that vegetable oil can wash off skin/clothes using cold water alone.

Have tried PEG 40, Tween 20 as well as Tween 80. All 3 do the job, but are very expensive. Are there any cheap alternatives?

Thank you!

No idea. And I know nothing about those 3 products. My first concern was environmental damage by surfactants. I found this in a horticultural discussion:

Alkyl polyglucosides. As complex as this term sounds, it simply refers to modified sugars. It has been found that some modified sugar molecules have surfactant-like properties and may be used as spreader/stickers. Although this class of adjuvant has been around for some time, it is only now becoming popular due to its organic origins, biodegradability, and the fact that it is environmentally friendly. There are low foaming and high foaming types, and many are very good wetting agents. Originally developed as environmentally safe cleaning agents (car wash cleaners) in England, they have transitioned to being used in laundry detergents and as agronomic adjuvants. These products have very low potential for phytotoxicity because they are derived from plant sugars. Research on these materials is on-going.