Which organization was established in May 1942, with a strength of 150,000 members serving in various capacities during World War II?

The organization established in May 1942, comprising 150,000 members who served in various capacities during World War II, is the Women's Army Auxiliary Corps (WAAC). This group was created to fill in roles that were necessary to support the military but did not involve direct combat.

The WAAC allowed women to take on a variety of important functions, including clerical work, signal work, and roles in transportation and logistics, thereby freeing up male soldiers for combat positions. The establishment of the corps marked a significant step towards the inclusion of women in the military at a time when their contributions were increasingly recognized as vital to the war effort. Many women joined with the hope of serving their country, and this organization laid the groundwork for future roles of women in the armed forces.

In contrast, the other organizations mentioned were established for different purposes: the Red Cross focuses on humanitarian efforts; the American Legion is a veterans' organization established in 1919; and the Women's Volunteer Corps was created for domestic service rather than military roles during the war.