A. We need to show that the nurses are protesting an action performed by someone else.
The nurses went on strike to protest their being overworked.
b. themselves being overworked
c. themselves as overworked
d. their overworking
e. overworking themselves
B/C-"Themselves" is the reflexive form of "they", "Their" is the possessive form of they. We need the possessive to attribute "being overworked" back to the nurses.
E makes it sound as though the nurses overworked themselves
D does not convey the action properly