The decade of the Great Depression was one of frantic creativity as many manufacturers pushed experimentation to the forefront in an effort to find sales in a stagnant market. This was especially true for the American automobile industry as can be seen by comparing cars from the beginning and conclusion of that economically dark decade.
Above are Chevrolets from 1930 and 1941. The 1930 model is a boxy assemblage of visually discrete parts (hood, passenger compartment, fenders, headlights, etc.) whereas the 1941 is integrated, smooth and lacks awkwardness.
Between those two model years was a transition where, feature by feature, car styling evolved from one convention to a distinctly different one. Below is a gallery of photos showing cars of various makes for model years 1935-38, the midpoint of the transition and the point where awkwardness was maximized.
Most of the cars look roughly similar. That's partly because General Motors was the acknowledged style leader (and had by far the largest market share) and the other companies tended to shy away from being too different from GM for fear sales might suffer. Other reasons were technical, having to do with learning how to shape steel sheets into compound-curve forms using mass-production methods -- something of little matter in the 1920s and earlier.