The error in this sentence is b: his/the staff.
The only time we use the slash is to write he/she or him/her. You could write “himself/herself.”
He told his staff that each of them should carry out the task himself/herself.
The servants are his either way.
The word himself should be used because you are talking about each person individually. It is okay that the male pronoun is used. In English, we often use the male pronoun as a neutral pronoun referring to either male or female.
This would be correct because each of the staff members is included, and the indefinite pronoun was used. Here is an example.
He told his staff that each of them should carry out the task himself.
One way to think about this is that “each” is singular, so it has to be matched with a singular reflexive pronoun (“himself” in this case). You could end it with “himself or herself” if you wanted to be gender neutral.