Right word to describe "people working together"?

Solution 1:

Team.

From my American English viewpoint, gang is frightening, and crew more subtly negative.

Work party sounds weird -- I associate party with a group of people waiting at a restaurant, a diplomatic delegation, or a group on an expedition.

Solution 2:

The clue to focus on is that these people are teachers, and taking classes. If they were labourers, gang or crew would be fine (gang does have some criminal overtones, but not enough to make it unusable); if they were press ganged to clear the road outside the college then work party would be normal, but professionals doing their job would prefer to be called a team.

Solution 3:

Like ash, I would go with team (A number of persons associated in some joint action), but for different reasons.

Gang suggests drug wars and the like ("Any band or company of persons who go about together or act in concert (chiefly in a bad or depreciatory sense, or associated with criminal societies)- OED), and even without them a gang was a bunch of labourers (A company of workmen - OED) which doesn't really suit your sentence.

Crew suggests a bunch of people running a ship, aircraft, or train or in more modern times a retail outlet of some sort, which again doesn't really fit your sentence.

W.ork party is more of an ad hoc thing. OED - "a group of people who come together to carry out a piece of work of mutual or social benefit". Maybe it is just my own experiences, but I tend to associate work party with voluntary and/or conservation work.

Solution 4:

Dean Shrivastava and his __ of twenty faculty members took care of the classes.

We need to look no further than the existing sentence for the right expression in the given context.

The phrase twenty faculty members already exists, and the fact need not be re-stated.

Dean Shrivastava and a faculty of twenty members took care of the classes.

Helpfully also, the referred Shrivastava happens to be the Dean, so that the other members might be "assigned" to him. (Except that his faculty could have other implications, the primary meaning of faculty being quite another thing.)

Dean Shrivastava and his faculty of twenty members took care of the classes.

Phrasing a sentence appropriately improves readability.