From Fallout Wikia:
United States Army:
Little is known about the status of the EAF before 2077, and it's not entirely out of the question that they might not have existed at all, with the Enclave controlling the United States government and Army. However, the Enclave presence of the Oil Rig indicates that at least some kind of a security force was present.
From Fallout Wikia:
United States Navy: Despite the fact that the Pacific Fleet was ordered to the Poseidon deep sea oil derrick on March 30, 2076, it is unknown if, after the War, the Enclave controls any operable US Navy warships. The fact that there are no sailors on the rig itself seems to indicate there are no ships currently docked there, perhaps because all remaining vessels had deteriorated beyond repair, and/or were cannibalized for parts.
United States Marine Corps:
No Official Cannon or Mention in the Fallout Series thus far.
United States Air Force:
No Official Cannon or Mention in the Fallout Series thus far.
My thoughts on the EAF's Organization and Structure:
Combat Branch:
Role: Involves reconnaissance, security, and other aspects of both offensive and defensive combat situations.
Administration Support Branch:
Role: Focuses on support jobs dealing with EAF personnel, administration, finance, legal, information and religious services.
Construction and Engineering Branch:
Role: Consists of jobs in every aspect of construction, including electrical, carpentry, masonry and plumbing, as well as heavy equipment operation and supervising construction engineering.
Intelligence & Combat Support Branch:
Role: These roles support EAF personnel involved directly in combat. They work behind-the-scenes to support and provide intelligence to Soldiers on the field.
Legal & Law Enforcement Branch:
Role: Focuses on keeping the people and property of the EAF safe.
Mechanics Branch:
Role: Tasked with keeping the EAF's vehicles and machines in proper running order.
Medical & Emergency Branch:
Role: Consists of jobs in the medical, dental and veterinary fields.
Transportation & Aviation Branch:
Role: These jobs involve the coordination and supervision of personnel, equipment and procedures for proper transportation and use of EAF materials throughout the world.
Special Forces Branch:
From Fallout Wikia:
Verti-assault Teams:
Arguably the most elite combat units, Vert-assault Teams are composed of crack Enclave troopers equipped with advanced power armor and heavy weaponry, described as "Usually they just go in shooting. They let someone else sift through the ashes to figure out what was going on.".
Special Duty Secondary MOS:
From Fallout Wikia:
Enclave Control Company:
A military company responsible for perimeter defense, their members are equipped with the best and most advanced weapons available to the Enclave and are a very versatile outfit.
(Note: Training for the ECC, probably resembles training currently received by Marines who are "Security Forces" or "Marine Security Guard" trained.)
Locations:
West Coast:
Camp Navarro
Recruitment Camp
Cybernetic Maintenance Facility
East Coast:
Raven Rock Military Complex (Site R)