What is the difference between "on the side of the road", "in the side of the road" and "at the side of the road"?
Well, they do seem interchangable to describe something unmoving. On is usually for animate things. To use at for an an animate it needs to be standing relatively still. You wait at(or on) the roadside for a bus because you aren't moving. But you only "walk on the road" because "at" implies a static location.
To be "in" there needs to be some an established barrier that surrounds so it defines "out". "In the road" makes me imagine the sides of the road as the barrier. But "in the side" doesn't work because it's only 1 barrier that does not surround. So in would mean a physical feature specific to the side of the road.
Thus Budda on the side of the road implies that he is walking on the sidewalk.
In the side of the road implies someone killed him already and stuck him in a gutter.
At the side of the road, and Budda is waiting for something, probably for a WALK sign.
"In the side of the road" only has 700 hits or so, and most of those describe potholes, indentations, ditches, and other physical features of the road. Most of the other references looked like grammatical errors that weren't caught for some reason.