which ICS functional area sets the incident objectives, strategies and priorities and has overall responsibility for the incident?

Answer: Incident Command.

ICS or Incident Command System refers to a management hierarchy that comes into force in times of major accidents, natural calamities or other emergencies.

ICS also provides a standardized framework for command, control and coordination of responses of people across multiple agencies, who deliver relief work in times of emergencies.

There are five functional areas in an ICS. They are:

Incident Command Operations Planning Logistics Finance/Administration

The incident command is responsible for setting incident objectives, strategies and priorities. It also has the overall responsibility for the incident.