How should I build the walls for a tiny house on a camper frame?
It depends what you're after &amp; if you'd "hope" to get an official Use &amp; Occupancy approval. Will you be hauling it around the nation (or locally) or just parking it on a piece of land to drag it into the Sun for the winter &amp; under the trees for summer?

If it's just a Glorified Shed Dwelling, then whatever your Local Building Dept. says is whom you have to please. So, they don't condemn it, fine you $10,000 &amp; destroy your masterpiece. Being a dwelling is what paints the bull's-eye on you. Everything will be legal &amp; fully inspected &amp; corrected until it passes as proper &amp; safe...or you can't live in it, period.

Otherwise, I agree with Ed Beal. A house is a house &amp; 2x4's 16"oc with 1/2" exterior plywood properly screwed are the minimum structural elements, for just the walls, that your Local Building Dept. will approve.

Toting this puppy on the road is a whole different issue &amp; your Dept. Of Transportation will have another set of requirements. Maybe, they want 1/2" plywood inside too for structural &amp; vehicle intrusion stability or 12"oc spacing or the building sealed with Poly Sheeting or all screws &amp; no nails.

Other people's Tiny's aren't your concern. They may not take them anywhere nor did it legal at all &amp; will pay the price for not building it proper with well proven &amp; tested materials, methods, procedures &amp; designs.

Here's a very loose Summary of CA's Notice to Tiny Housers

Here's the Full Notice from CA, directing you to their Uniform Construction Codes