Photography

Infrared imagery?

You could use the ol’ cliche’ infrared filter but you might get points deducted.

Go check out old cinematic tricks like forced perspective, foreground and background miniatures, and the peppers ghost illusion. Plenty of great guides online, plus they're all easy and cheap.

Consider using physical objects as a lens/shield/filter that warps the way the world looks. Could be warping in terms of colour (e.g. colour filter, IR filter), or space (e.g. mirrors, "compound eyes" like in flies could be simulated with multiple pieces of glass, etc.).

And you'd probably have to find physical locations where you get inspired with "Damn this looks out of this world".

I agree with the rest in that this is pushing you for creativity and innovation.

One precise shot I would go for is Interstellar's Cooper Station. Everything looks warped, the land is both beneath you and above you. We have seen shots like this taken with some fancy 360 degree cameras, right? How can we do that using a regular camera and using physical objects (round glass? idk) to make space look warped?

Put some colored plastic or gel in front of the lens and you'll get a strong vibe already. An example would be photos taken in red&black or blue&black etc. It will creare an atmosphere and it could be in that world the light that shines closer to the red or blue spectrum and thus you have those kind of colors. You can also put elements which are strange and out of place, like an aura around people which you can obtain with light effects, double exposures or other ways other than Photoshop. Or people in this universe have halos above their head. Or objects and/or people can walk through solid matter. Easy example would be a double exposure made in the corridor of your house where you seem to walk through a wall. Or people walking on air, or swimming through air, or sliding instead of walking. Or you can make it so that in this parallel world thought streams, or thought forms are visible. Slow shutter speed and you use long plastic strings and pull them, or some festoons, and it will appear as if a sort of colored beams are traveling around. Like two people in a room, and sort of beams or clouds moving between them as if they're communicating through their mind.

Or you can use strange things that don't make sense. An example would be a sort of family photo but the person in the middle is sitting in deep meditation and there's floating stuff around. Or you can show it's a parallel world by using our current technology plus things that doesn't exist yet. An example would be your living room, except there is a sort of floating surface on top of which stands your abat-jour. A sort of floating lamp. You can do that without Photoshop. Just find something.