Very, very sad history.
Let's get to the meat of this: The bullet points. (I love bullet points.)
- Martian Manhunter is an alien being who just happens to look vaguely human.
- Martian Manhunter is insanely powerful.
- Martian Manhunter is relatively poorly known except to fairly hardcore comics fans. (Yes, this really is part of the character.)
- Few if any writers know or care much about Martian Manhunter, so he tends to get written as a wimp and smacked around a lot.
For a good amount of documentation on Martian Manhunter of all kinds, there are two good blogs, Every Day is Like Wednesday (already linked, although you'll have to dig into the archives, as it's been a while) and The Idol-Head of Diabolu (a very Manhunter-centric blog). This is ultimately where I've learned most of what I know about him.
With regards to J'onn J'onnz's alien-ness (by the way, if you don't know, that's pronounced "John Jones"-chalk one up to comic book silliness), J'onn J'onnz, in one story, became addicted to pseudo-Oreo cookies, and then, in order to cure himself of this addiction (it was an actual drug addiction with physiological symptoms, not a psychological one), he purged himself of his addicted cells and fried them with his heat vision. You don't really get much more alien and weird than that.
With regards to his insane power levels, well, he has super strength, super resistance to injury (I hesitate to call it invulnerability), super speed, telepathy (powerful enough to launch a psychic attack on a small army while dying), telekinesis (he can use the powers of the universe to create an ice cream cone), intangibility, invisibility, heat vision, shape shifting, extreme regeneration (he can grow a new everything, and once grew a new person out of himself-it was a human named John Jones), and in his early Silver Age comic appearances, the ability to snap his fingers to do almost anything. (I am so not making this up.) On one occasion, he totally mauls (note: scroll down a bit for what I'm linking to-it's the third picture down) a guy with pretty much all the powers of Superman and then some. On one occasion, Superman listed Martian Manhunter at the top of the list of beings on Earth he'd be afraid to face in battle. His only weakness is to fire (what), and that pretty much only works when the writer feels like it.
With regards to his obscurity-well, he's shown up in two or maybe three cartoons, once as a brief cameo and another time as a major character for most of the run, albeit a toned down, less interesting version of himself. He has not had his own title in decades, and his runs in comics are generally either short or purely as a supporting cast member. And so hardly anyone knows who he is, other than pretty hardcore comic book fans and trivia fiends (of which I am the latter).
With regards to the last point-well, it's pretty much the Henry Pym effect. While good ol' Pym has, apparently, managed to crawl out from under this particular rock for the moment, at least for the purposes of one author, Martian Manhunter has recently been killed over it. (Don't worry-he'll probably get better.) Of course, this is a corollary of point #3, as well, as Martian Manhunter dying doesn't keep comic books from being sold.
And really, we come to the crux of what I'm driving at-choosing to kill Martian Manhunter was a lazy answer to the question "How do we make the latest crossover look like Serious Business?"