It's a lot easier to classify the above joke than to say exactly why people would laugh at it. It's correctly identified as a "sick joke," but that's not all it is. If the character just stood there and said that he put 14-year olds in a blender, it probably wouldn't be funny. Or else it would, but for a completely different reason.
As it is, the joke springs a surprise that hinges on the ambiguity of the phrase "all over me." An expectation is set up in the first panel according to an interpretation of "all over me" that is reasonable in the context. The expectation is then violated by revealing a different context and a different meaning. This figure of speech is called paraprosdokian, and the most infamous example in the English language is probably Henny Youngman's "take my wife, please."
The sickness of the joke adds emotional impetus, I think, while making another unexpected connection between the morbid subject matter and the context of telling a joke.
People can be counted on to laugh at such jokes, but nobody is sure exactly why. Freud put it down to discharge of energy upon recognition of the unconscious, or something like that. Sounds like bullshit to me.
I lean toward explanations like Marvin Minsky's or Edward de Bono's. They propose (to paraphrase very roughly) that laughter plays a role in learning and brain development. The way I would say it is that jokes and humor make new connections in the brain by setting up expectations and then violating them as in the above example. Making new neural connections is useful to humans-- that is, from an evolutionary standpoint, human beings who make more neural connections have more viable offspring. They are smarter, basically.
The pleasure that humans experience in these new neural connections is called "humor," and it motivates them to seek out jokes in the same way that sweetness motivates them to seek out fruit or sexual pleasure motivates them to seek out a hot fuck. Laughter is natural selection's way of getting us to exercise our brains.
That's how I see it, anyway.