A list of some of the units that participated in the 1937 campaign in Shanxi (note the presence of Hideki Tojo, who would later become PM, was a leader of the Kwantung Army forces):

http://en.wikipedia.org/wiki/Order_of_Battle_of_the_Battle_of_Taiyuan

I would guess that many units were rotated in and out of the area between 1937 and 1945, so it would be hard to list them all without doing some archival work.

If you are interested in the experience of the Japanese soldiers, a documentary called "The Ants" was released in Japan a few years ago. It tells the story of surviving Japanese soldiers who, at the end of the war, were ordered by their officers to join the Nationalist forces in Shanxi and participate in the Chinese Civil War.

Hello there! You may want to consult the Japanese Monographs, specifically monographs 72 (see esp. pp. 122ff.) and 178, both of which deal with operations in North China. I unfortunately don't have time to flip through them and extract all the data for you.

You can also find Chinese orders of battle and some information on Japanese troop movements in History of the Sino-Japanese War (1937-1945), 2nd ed. (Taipei: Chung Wu, 1972), which is an abridged (though still painfully detailed) translation of the official histories of the KMT. Be warned: the information is quite spread out.

As a last resort, you can try to search up which officers were assigned to the area via Generals.dk