[I'm cheating a little on this one. I found no interesting X so I'm using EX]
Exercise — a military maneuver or simulated wartime operation involving planning, preparation, and execution, for the purpose of training and evaluation.
Exfiltration — the removal of personnel from areas under enemy control by stealth, deception, surprise, or clandestine means.
Expedition — a military operation conducted by an armed force to accomplish a specific objective in a foreign country.
Explosive ordnance disposal — the detection, identification, evaluation, rendering safe, recovery, and final disposal of unexploded explosive ordnance. Also called EOD. At one point my son applied for this job. Mommy was NOT happy.
Extra Military Instruction - EMI. A supposed learning opportunity for a serviceman to better learn some military instruction. Usually a non-judicial punishment consisting of some menial task like running in place with arms outstretched from the chest while holding a rifle (Army) or changing into every uniform once an hour for inspection (a "Fashion Show") (Navy).