So there’s a lot of ways you can achieve this kind of thing, but it’s primarily going to be either software plugins, or physical hardware that plugins are simulating (of the two, software plugins are typically cheaper). A lot of the common tools originate more from the music industry side of things. There’s some “common” classic effects like flangers, phasers, and distortion that have been around for decades, and basically are the building blocks of old-school rock and electronic music.
There’s a ton of companies and people making plugins, but here’s three popular brands. It might be overwhelming at first, but these are some good places to start browsing to get an idea of what’s available! I know Waves has demo videos for a lot of their plugins, and all three may offer demos. They also all probably have mailing lists, which is often how I find out about new releases.
For a couple more specific examples, Absynth can produce some really interesting textures. It comes with a lot of presets, but you can import any sample and then manipulate it to get some interesting, though very unpredictable, results. I used to create a lot of the energy sounds in this short, and Absyth was also used on a sample of an eagle to create this ship from Rogue One.
In kind of a similar fashion, Zynaptiq’s Morph lets you combine two sounds together in ways that can be pretty cool; Mick Gordon used it on the new Doom soundtrack to blend a chainsaw with a guitar.
You can get some really cool textures with Paul’s Extreme Sound Stretch, which is totally free.
There’s tons of stuff out there, but I hope that helps at least as a starting point!