U.S. Postal inspectors rightly carry firearms, because one of their duties is investigating the movement of contraband via the mails, i.e. narcotics, weapons, "anthrax", and as a consequence arrest these suspects and also serve search warrants.
As far as the Departments of Education and Labor, who knows.
The USDA includes the U.S. Forest Service. They employ Special Agents and other law enforcement personnel who investigate crimes on National Forests. These crimes include murder, rape, and drug violations.