Here's a link to the 1938 Shop Manual. Here on page 3, they specify Hypoid oil for the rearend.
http://chevy.oldcarmanualproject.com/shop/1938/38csm003.htmlOn page 7 they give the specs for Transmission fluid. Depending on conditions, they specify 140, 160, Sae 90, 40 weight motor oil, and even Sae 90 blended with kerosene for winter months.
The Lube King version (Big R, Farm and Home, Farm King) of GL1 states that SAE 90 is the same as Non-Detergent 40 weight.