What is the origin of this weird looking facial feature/mask?
The face on the first picture comes from Hyottoko, which according to wikipedia is:

a comical Japanese character, portrayed through the use of a mask. His mouth is puckered and skewed to one side. Some masks have different eye sizes between the left and right eyes. He is often wearing a scarf around his head (usually white with blue dots).

The reason for it to be commonly used extends beyond anime and manga, though, as it is a common stock character in other media — such as theater — too:

Hyottoko seems to have been a legendary character in Japan in the past, and is now a stock character.

The reason why its features are the way they are, albeit exaggerated, is explained by its name too:

The origin of the name comes from &quot;fire&quot; (火, hi) and &quot;man&quot; (男, otoko), because the character is blowing fire with a bamboo pipe, hence the shape of the mouth.


I don't think Suneo's expression is supposed to be an adaptation of the mask or what it tries to convey, though I don't have anything to back that up with.