I'm not sure if this will be of any help, but I assume this would change depending on what other materials were used in the walls. For example, if the culture has metal nails, that might change things.
On earth today, modern societies can still build very large structures using these materials. For example:
But, I doubt if such feats could easily be achieved 1,000, 10,000 or 100,000 years ago by all people of all economic classes, due to lack of computer-aided architectural planning, modern quality control of materials used, and all the accumulated architectural knowledge over time. Even if they could make it in previous times, they might need other advanced technology such as scaffolding, cranes, masonry, metallurgy, etc. to make such building possible.
With all three materials, I assume the type of materials used would also greatly effect the thickness of the walls. For example, very weak woods like balsa would need to be very different thicknesses than woods made of Australian Buloke, which is considered to be the strongest wood on earth. The same would apply to stone: walls made of talc would be different thicknesses than diamond walls, or granite vs. limestone. With adobe, I imagine the same would hold true. However, I did find this quote about adobe building code in the US:
Adobe walls are load bearing, i.e. they carry their own weight into the foundation rather than by another structure, hence the adobe must have sufficient compressive strength. In the United States, most building codes call for a minimum compressive strength of 300 lbf/in2 (2.07 newton/mm2) for the adobe block. Adobe construction should be designed so as to avoid lateral structural loads that would cause bending loads. The building codes require the building sustain a 1 g lateral acceleration earthquake load. Such an acceleration will cause lateral loads on the walls, resulting in shear and bending and inducing tensile stresses. To withstand such loads, the codes typically call for a tensile modulus of rupture strength of at least 50 lbf/in2 (0.345 newton/mm2) for the finished block.
This might not be exactly what you are asking about, but in a sense, it might not be able to be avoided in a natural setting, namely other needs the wall must meet. For example, most walls need to do more than just hold up the roof or second floor. As you mentioned, medieval walls needed to provide defense, and modern walls need to house electrical wiring.
If the building is in a very cold climate, insulation may be needed, and so if the insulation is placed inside the walls, that could change structural requirements. Or, as you mentioned, defense against hostile entities historically has changed walls. Or, earthquake prone regions would require different styles of walls. Frequent flooding, excessive heat, high winds, etc. would also effect wall structures.