Ohhh, where to start...
I've done some esoteric research from time to time because of work, like a lot of astrophysics and theoretical engineering for a mecha sci-fi videogame. Which also included going in deep to military tactics and reading papers about theoretical war strategies in case of an actual military conflict in orbit. (For the game Phantom Galaxies)
Another occasion I delved deep into biology, studying the inner workings of organs to help design levels based on the organs of a massive space creature (For the game Project Tartarus, still in development)
For Obey Me, another game, I went into heavy demonology and other weird mystic crap to create a urban fantasy setting for the game.
For my novel, one of the weirdest things I did (And thankfully stopped, because it was taking over my life) was studying the origin of weapons. I fell into a rabbit's hole of history and weapons, as my logic at the time was "Wait, my fantasy world isn't the real world, so how did a sword or an axe become the go-to weapon, wouldn't it make a lot of sense to have different weapons?" A lot of that survived in the really unhealthy obsession of the Morbani with developing new swords and weapons.
But the weirdest and most depraved thing I ever had to research for a job was when I worked on a Garfield Mobile game.
I read all of Garfield in one week, every strip, special and extra comic-book. I wasn't the same man after I finished, I was scarred and damaged for life.