What is the name of this black lines only oriental drawing style?

The technique seems to be woodblock printing.
You can tell by the linearity of the drawing, the lack of large dark areas, and the wavy structure of the lines. Especially the second picture shows the underlying wood nerves, as adjacent lines have the same slight deviation.

Not very oriental sounding, I know.

The Japanese term for woodblock printing is mokuhanga, and stylistically, the images can be considered a form of ukiyo-e, which until the early 18th century were done in black and white, and of which the linework is iconic:

The earliest prints were monochromatic, and these lines were the only printed element; even with the advent of colour this characteristic line continued to dominate.
^source

Hokusai and Hiroshige are its most famous exponents.