Classified as a category 4 threat, the Elib is somewhere between a vampire lord and Godzilla for limits of escalation. Yes, I would consider using a nuclear device to kill just one. I am that sure that I want it dead.
At regular intervals, a god takes control of your world's weather. Choose the gods at random each turn of the interval and begin applying their effects subtly. Their power will depend on the strength of those who worship them.
For civilised people, worship of a god actually wanes during that god's month in an effort to reduce their potential destructive effect.