There are tonnes of classic games that are just weird in general.
Albion -
https://www.gog.com/game/albion Sci-fantasy story with a perspective that swaps between first person and over the head console style isometric. Controls almost entire with the mouse, but with numpad controls for some of it.
Anachronox -
http://store.steampowered.com/app/242940/Anachronox/ Super interesting Sci-fi J-style RPG made by a western studio. Lots of strange camera tricks that work with aplomb to set the world into feeling like something that's just entirely off the chains.
Darklands -
https://www.gog.com/game/darklands One of my all time favorite classics, just the character creation is likely to confuse the fuck out of a lot of people. But it stands up to the test of time as one of the more complex games, and one of the games that a lot of modern complex games generally reference as a grounding post, or an inspiration for their development.
Elder Scrolls Morrowind -
https://www.gog.com/game/the_elder_scrolls_iii_morrowind_goty_edition Aesthetic is just weird here. Sent from an unknown land to the island of Morrowind, you explore through environments that are at once strange and familiar. From swamps too mushroom forests, to giant mushroom towers that require spells and magic to navigate because they are run by assholes. Seriously was one of my favorite games as a kid give it a try. And if you use the graphics extender, set the cell distance to something lower than 4. Morrowind is actually best if you can't see what's coming from 10 cells away.
Neverwinter Nights 2 Mask of the Betrayer Just play it, no spoilers, beyond that it picks up after the end, but is almost totally disconnected from Neverwinter Nights 2's Original Campaign. It's weird, but one of the few games that has done the themes it has right.
In modern games.
SOMA - No spoilers for this one again. Google it up, play it, it's crazy good, as an adventure game. It's themes are harsh, scary and horribly amazing at making you think. Your own as in the player playing the game's mortality will be brought into question.
Tacoma - The other side to SOMA's creepyness. Brighter, more simple but still examining a lot of the same themes. An art piece but an amazingly structured, and strange one. Another that's just best to jump in and play.
I think that's enough.