I think I've seen all or nearly all his military-themed characters now, and had some thoughts about them. Would be curious to see other people's thoughts on the subject.
Jesse James in "Kansas Raiders": Jesse is technically a Civil War era guerilla. He has a shell-shocked quality due to some events in his past, which Murphy conveys very well, for obvious reasons. Jesse is described in the movie as a good leader and tactician, but the weak script doesn't really support this idea well-you're pretty much just supposed to buy it because Jesse is being played by a competent small-unit leader and tactician. These reputed qualities of Jesse, together with his discomfort at the nastier aspects of guerilla warfare, make it seem like he'd be happier in the regular army.
The Youth in "Red Badge of Courage": Ok, so this movie isn't most people's idea of a good time, and nobody except John Huston urgently wanted to see the "toughest soldier in the 3rd Infantry Division" as a whiny deserter who grows up and returns to the fray. But to hear about Murphy's insistence on fear as something a soldier has to live with, and work past ("I'm scared sick before every battle") and then to see him actually demonstrate it onscreen in this film is really something.
Lt. Jed Sayre in "Column South": Sayre is the first of a series of frontier Cavalry officers that Murphy would play, all fiercely determined to do the right thing according to their own unconventional codes, even if it means defying orders. Sayre is perhaps the most conventionally likable: reserved but witty, sympathetic towards the Indians, dignified and honorable, but not above using a game of poker to catch a murderer. He also represents the first break with the "juvenile delinquents/outlaws" and "misunderstood young men on the verge of becoming delinquents/outlaws" that dominate Murphy's early lead roles.
Private/Corporal/Sergeant/Lieutenant Audie Murphy in "To Hell and Back": I kind of sympathize with Spec McClure's complaint that we're seeing an overly idealized and mellow take on the feisty teenager with the hard-luck childhood who earned all those medals. But, hey, what else do you expect from fifties Hollywood, and a man of thirty-something playing his younger self? Mid-fifties Murphy was I think still a troubled man but surely in some ways wiser and more experienced than his WWII self, and I think that shows through in this movie.
Private John Woodley in "Joe Butterfly": A lot of people didn't care for this performance at the time, but I find it kind of interesting because I can imagine Murphy turning into this kind of casual troublemaker if his superiors had managed to keep him out of the combat zone. He had a shrewd mind, a hatred of boredom, and his postwar life would show that he enjoyed poking the hornets' nests to see what would come out.
Lt. Frank Hewitt in "Guns of Fort Petticoat": probably the most generic of Murphy's cavalry officers-he's mostly defined by his refusal to be a party to his superior's war crimes and his tough love towards his "subordinates." I suspect the chance to show civilian America what the personality and authority dynamics inside a small unit are what mostly attracted him to this project.
Craig Benson in "Battle at Bloody Beach": This character is technically a civilian employed by the navy to assess and supply guerillas in the Philippines (a really cool idea that the film doesn't do enough with, IMO). But he is working for the military in wartime, so, we'll cover him here. Probably Benson's most Murphy-esque moment is when he rebukes the guerilla leader for trying to make a heroic last stand that will get the civilians killed, and the aftermath of that, where Benson tries to find (and eventually does find) a solution that puts his own life on the line rather than everyone else's. I am unconvinced by Benson's claims that he'd retire from the war effort the moment he recovers his longlost wife: he comes off as somewhat jaded about what he does, but not that jaded, and it's hard to imagine Murphy walking away from a fight.
Captain Jeff Stanton in "Apache Rifles": This is a really excellent portrayal of a rather grim and flawed but deeply honorable man. He doesn't, aside from the grimness and the sense of honor, strike me as being all that much like the man playing him. Except maybe the mad ninja skills he shows late in the movie.

And that scene where he punches out L.Q. Jones for insulting his girlfriend. That flash in the eyes...that sudden right hook...I suspect a lot of the stories about Murphy overzealously defending his friends looked like that to the third-party observers.
Captain Bruce Coburn in "40 Guns to Apache Pass": I've seen Willard Willingham quoted as saying this is the one role he wrote for Murphy that he felt really captured the essence of his friend. Like the man playing him, Coburn has a battlefield commission (which he is deeply proud of), an idealistic loyalty to the Army, a fierce temper and a ruthless attitude towards insubordinate or cowardly conduct.