I've actually been running a similarly themed game off and on like Hellboy in Monster of the Week. Though I've used creepypasta monsters as the baddies and threats.
Aw man, how is Monster of the Week? It looks real fun.
*cough*HELLBOY*cough*
...this is relevant to my interests
RIGHT??? A Hellboy/Hellblazer/Dr. Mirage style of game would be
awesome.
Either way, a few systems you could look into is: WT Cerebus Club (its is more Victorian than WT and is a bit more suited to the CH feels), Fear Itself (and other systems) have psychic powers and you could add "bonus points" for super powers.
Well, like I said, I have next to no experience running occult oriented games. I only have stacks of comic books about superheroes fighting demons and slinging spells at Lovecraftian horrors. I don't think I'd be up for running something like this; the idea of it is just cool.
Another big question you need to answer is "Why Superheros and not just Heros?"
Because I love superheroes even more than Max loves anime. Also,
Justice League Dark and
Dr. Mirage, the examples I listed, are both comprised of superheroes. In JLD, you have John Constantine, Deadman, Zatanna, Swamp Thing, and Madame Xanadu as the core cast of characters. With the exception of Deadman (who is a ghost) and Swamp Thing (who is spooky), these are all characters with a public presence. In fact, being a superhero builds up their reputation, which in turn brings money into their day jobs (John Constantine the private investigator, Zatanna the stage performer, and Madame Xanadu the occult saleswoman). Swamp Thing and Deadman are both flashy in everything they do just 'cause that's how they are.
In
Dr. Mirage, the titular hero is a television medium that is so widely regarded as legit that no one in the world is a skeptic about it. She solves crimes via talking to ghosts, and she's basically pissed off so many poltergeists, demons, and other sort of shit, and then got filmed laying down some crazy magic to shut them out, that everyone and their mother is like, "Dr. Mirage? Holy hell, she is the bee's knees." Granted, this is my first foray into the Valiant comics universe, so I don't exactly know just how bonkers the world is for the average joe to be like, "yeah man, ghosts and demons and shit, totally legit," but I'm pretty sure it's crazytown. But yeah, being a superhero pays the bills for her.