Answer:
D. The workman directed the drivers and us around the road construction.
Step-by-step explanation:
The list of objective case pronouns includes:
me, him her, it, you, us, them. 
In a sentence, they should be used as objects. 
Option A uses him as a subject, which is incorrect. 
Option B uses her as a subject, which is incorrect. 
Option C uses him as a predicate nominative, i.e. a subject complement, which is also incorrect. 
Only option D correctly uses an objective case pronoun, us, as an object.