Kieli

Kieli, a lonely girl with the power to see ghosts, encounters a man named Harvey, who happens to be one of the legendary Undying. The Undying were soldiers made from recycled corpses that were trained to be immortal killing machines in a violent war 80 years ago. She follows Harvey on his journey to return the ghost of a soldier, who died in that war and has since been a possessing a radio, to his grave.

A nine-volume Light Novel series written by Yukako Kabei. The first novel was adapted into a two-volume Manga illustrated by Shiori Teshirogi and released in English by Yen Press. Yen Press is also publishing the novels; the first six are presently available:

Kieli Volume 1 - The Dead Sleep in the Wilderness
Kieli Volume 2 - White Wake on the Sand
Kieli Volume 3 - Prisoners Bound for Another Planet
Kieli Volume 4 - Long Night Beside a Deep Pool
Kieli Volume 5 - The Sunlit Garden Where it Began Part 1
Kieli Volume 6 - The Sunlit Garden Where it Began Part 2

Tropes used in Kieli include:

Belief Makes You Stupid: Kieli believes this.
Blessed with Suck
Broken Bird: Kieli.
Church Militant: The Undying at first.
Conveniently an Orphan: Kieli and Harvey (although he may not count because he's dead)
Crossing the Desert: In the second novel, White Wake on the Sand.
Cruel and Unusual Death: Happens all the time in this series. Every other ghost that the three meet has come to an untimely end in some really, really horrible way.
- and later Jude. Although since he is reanimated with an experimental core technically he's not dead
Cute Ghost Girl: Becca
Cursed with Awesome: The undying, being immortal and all that.
Dead All Along: Becca as well as Tadai
Death Seeker: Harvey, and to an extent, the Corporal. They get better.
Dogged Nice Guy: Julius.
Good Thing You Can Heal : The Undying. Especially Harvey who has been shot, stabbed, burned, blown to pieces, crushed, impaled, hit by a car, run over by a train... the list goes on an on.
Forgets to Eat: Harvey, mostly because he doesn't have to eat. Corporal explains it to Kieli in the first book. Although later he starts to avoid eating all together. And after hearing the conversation between the two men who were disposing the corpses of the failed experiments who can blame him?
Half the Man He Used To Be: This happens to the Undying quite a bit.
Haunted Technology: The Corporal.
Heart Drive: Harvey's core gives him nearly unlimited healing powers as well as immortal "life" but if it's ever removed from his body he goes back to being well, ... dead.
Hoist by His Own Petard: Happened to the town of Toulouse. When they burned Beatrix at the stake, the town caught on fire.
Important Haircut: Kieli at the end of the first novel.
Immortality Begins At Twenty: Kieli and Becca believe Harvey is in college when they first meet him.
I See Dead People: Kieli.
- The Undying can also see ghosts.
Light Is Not Good: The church's Undying hunting corps. The soldiers are dressed in all white armor and both Kieli and Harvey say that they remind them of demons.
Lonely Rich Kid: Julius
Mayfly-December Romance
Monster Clown: A rare sympathetic version, he's also a Non-Ironic Clown.
My Name Is Not Herbie
Our Zombies Are Different
Razor Wind: The Corporal's method of attacking.
Running Gag: The Corporal always tends to call Harvey by the wrong name. More specifically, "Herbie."
Smoking Is Cool: Harvey. Enough said.
The Cynic: Harvey, all the way. Although he's trying to get better.
The Stoic: Also Harvey, due largely from his training and the fact that he's a Shell-Shocked Veteran
Time Skip: Of a year and a half in the fourth novel.
Tranquil Fury: You do not want to make Harvey angry to the point that he gets like this.
Used Future
Walking the Earth
Who Wants to Live Forever?: A big theme of the series, in the beginning Harvey is basically waiting around to die. And at the end of volume 4, when Harvey is telling the Corporal about the crack in his core, he actually seems relieved at the idea that he'll (probably) die the next time he gets a fatal injury