Answer:
Best: Option 4
Worst: Option 1
Step-by-step explanation:
The co-worker might be oblivious to the detrimental effect of his actions on work atmosphere. Talking to him and telling him to stop is the first step to improve this.
Option 2 is not as effective, as the co-worker would not know the reason and might just talk behind people's backs to other people, thus no actual progress would be made, except less communication overall.
Option 3 is likely to antagonize people, with the engineers being unhappy about your co-worker, and the co-worker being mad at you for telling on him. This option is the most likely to end up with someone leaving the job.
Option 1 is just expanding the circle of bad behavior, hence probably the worst possible.