Known collectively as "The Big Four" American thrash metal acts are the bands Anthrax, Megadeth, Metallica, and Slayer. I'm grouping these together since I'm only going with a couple examples from each. Although most of their songs are themed around the supernatural or occult, particularly Slayer and Metallica, there's also a song or two about comic book characters and sci-fi themes. So let's start with those.
Books (including comic books):
I don't think I need to say who Anthrax's "I am the Law" is about, do I? (psst, it's about Judge Dredd).
Anthrax are also Stephen King fans, and their song Among The Living is about Randal Flagg from The Stand. They also have one based on Apt Pupil but that's not really genre fiction.
According to the notes in the CD liner, this Megadeth song was written about The Punisher:
And Five Magics is probably their most fantasy-heavy song, inspired by the book Master of the Five Magics (although they changed what some of those magics are in the song):
Whether or not you personally consider it fiction, some of the Bible's stories are "super" in their nature, and Metallica's song the Four Horsemen is based on their story from the Bible, and the characters have been used in plenty of genre fiction, as any Supernatural fan would know (although two of their horsemen are named differently. Song: Time, Famine, Pestilence and Death. Bible: Conquest, War, Famine and Death).
This song is based on the story of Moses, mostly from the movie The Ten Commandments, but since that movie was based on the Bible story, I'm including it under "books":
And someone was cool enough to post a video of the song using scenes from the movie:
Megadeth covers sci-fi with songs like Hangar 18 & Psychotron
Finally, we have the occult/supernatural:
Metallica has an instrumental inspired by many a fan's favorite elder one (they spell its name Ktulu)
Slayer's Raining Blood is about a soul trapped in Purgatory after being cast from Heaven and wanting revenge. Almost sounds like an episode of Supernatural.
Dead Skin Mask is about a real life killer (Ed Gein) who was the inspiration for fictional characters Norman Bates (Psycho), Leatherface (Texas Chainsaw Massacre) and Buffalo Bill (Silence of the Lambs). And is also just a plain creepy song.