Usually the animation contains a few moving 2D layers that make pseudo 3D effect. I'm looking for the name of this technique and any tools/services/frameworks/tutorials that may help me to make such an animation.
Please have a look at these examples:
https://dribbble.com/shots/2565628-Joysticks-n-Sliders-Test
Tradittionally this was done with paper, thus the name was paper cutout animation. Though when you go digital it is just known as cutout animation, and you have some more leway into stacking the images.
Any animation tool out there can do this. Including your browser.
I don't think there's a specific name for this style; it's a 2D animation with flat colors that emulate 3D movement.
It can be done with 3D software and rendered with a flat color 2D shader (toon shader) or use a 2D animation tool that just deforms the objects to mimic a 3D object - the very examples you provide use a script for After Effects to rig characters in such manner. With a clever use of masks you can make objects look like they're rotating in a 3D environment.
