Either is correct, depending on the intended meaning.
1) I wonder why or how someone could kill a person.
This is asking two questions, of course. The first is: "I wonder why someone could kill a person.". This is a somewhat odd question if taken literally. The appropriate (though rather trite) response might be "Because we are all physical beings and are thus capable of killing."
The second question is: "I wonder how someone could kill a person.". To this, a valid response might be, "With the use of a weapon such as a gun or knife, or one of various other means.".
2) I wonder why or how someone would kill a person.
Again, taking the first question: "I wonder why someone would kill a person.". To this, a valid response might be, "Perhaps because that person is an enemy in war.".
The second question being, of course: "I wonder how someone would kill a person." This is quite similar to the second question of version 1, though with a subtle difference. It implies a specific intention that someone would kill another person, or similarly, what would be a likely means of killing.
Finally, the order of why and how is not really a matter of grammar, so either way round is acceptable. However, I would tend to put how first as it is the more direct/superficial interrogative.