The military does not utilize one specific martial art that exists outside of the military. The green berets will have undergone training in grappling as well as striking, disarming and other CQC (close quarters combat) techniques. Note that their training is not oriented towards winning tournaments, fighting with gloves, or just roughing up some guy at a bar - they are trained to kill, disable, submissify.
The closest single styles of Martial Arts to what the American military uses (at any given level) are Krav Maga and Sambo (which are related). Krav Maga is the martial art that was developed and is utilized by the Israeli military (standard and special forces). (Combat) Sambo is the martial art that was developed and is utilized by the Russian military (standard and special forces). There is also sport Sambo, which is obviously different.
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If it is a weapon, it can be found in the martial arts. The skills and mental attitude related to the use of any weapon is a martial art.
Kabudo is the martial art that teaches the use of traditional martial arts weapons including the sai. Some karate schools include kabudo in their standard curriculum.
Sasuke from Naruto? He doesn't do martial arts, he just uses fantasy stuff...
There are many martial arts that use the bo. Kungfu and kobudo are two of them.