I'm running a campaign for some close friends and their only request was 'make it weird' so here I am. I've got the bones of the world down, it just needs fleshing out so if you have any kind of bananas ideas for creatures, magic items, backgrounds and all that lot, shoot. Thank you

I freaked my players out with a flock of flumpfs.  I also have a region where the landscape randomly shifts (roll a d4, 1 is grassland, 2 is desert, 3 is mountains, 4 is forest) usually I roll once for every hour of travel and at the end of tests.

What are they looking for in terms of "weird?"

Do they want stuff like flumpfs (as listed above)? Or do they want more stuff like the outer planes? Do they want mix-and-match genres? Like cowboys vs. wizards vs. stormtroopers?

Lots of things might classify as "weird" -- do you have any more for us?

May not be weird but the wacky wasteland encounters from fallout could do the job with a little tweaking, the wiki has a full list:

https://fallout.fandom.com/wiki/Wild_Wasteland

oh, that's really cool and will make our campaign kinda nuts but I love it! Thank you!

Everyone is a bunny (except the PCs who are from another plane), using that UA.

Inanimate objects can talk ( rocks, tables, etc.) They generally choose not to, but can be convinced with the proper motivation.

Or, just update Dark Sun.

Quote from Twokthethird >>

I'm running a campaign for some close friends and their only request was 'make it weird' so here I am. I've got the bones of the world down, it just needs fleshing out so if you have any kind of bananas ideas for creatures, magic items, backgrounds and all that lot, shoot. Thank you

The main characters are the center of everyone else's attention.  Wherever they go, everyone around them is always paying attention to them - watching, staring, listening.  None of them invade the PC's personal space, and if pressed on why they're doing this, NPCs express confusion - the party is just so interesting, why wouldn't they pay attention to them?

Random bigby's hands floating around disparately in a flat plain. No one knows the source, and there are no animals here. Stick around and find out why, if you don't care about your or your companions' lives.

Random is a good way to get some weird. Fluctuating gravity, maybe sometimes its 10% more or less. Not all the time but once a day it goes floppy for a few minutes? or light and dark isn't predictable, maybe eclipses at odd times every few hours or days. magical effects are variably 25% less effective or 25% more effective. dimension shifts. time slips. you don't want to make it a pain to DM it. you could create a chart with various combinations and just roll a d8 or d12 or whatever and make up the duration or vice versa.

Wutcha think?

There are weird parts of my world that flip your stats. Physical stats become mental and vice versa. E.g. Con <-> Wis, Str <-> Cha, Dex <-> Int.

Read the Manifestoes of Surrealsim by Andre Breton until you can distill Hunter S. Thompson's quip "When the going gets weird, the weird turn pro" into an understanding you can act on.  

Seriously, problem with weird is that it's eccentric but also accessible.  Just spewing rando nonsense you got elsewhere will get messy and ultimately boring fast unless you have a "logic" to your "illogic."  Watch some David Lynch movies, Twin Peaks Black Lodge arc could easily become a campaign.  The best weird's can't be parsed in terms of there's this dynamic or mechanic.  There needs to be another feeling you're actually going for underpinning or overpinning the little tricks.

My homebrew game world is pretty weird, but I'm really versed and read and view deep in weird.  Some of us in this forum were doing one paragraph game world descriptions.  Abandominion has a lot of debt to Emerson Lake and Palmer.  You don't have to like the music, just take the lyrics to "Karneval #9 First Impression" and make that an encounter and build out from there.  

When I was in college I ran a campaign in a world called  Bob's World.  The concept (unknown to anyone living on the world)  an omnipotent omniscient but not very creative being decided to build his own world but didn't have any good ideas so he looked for and copied "interesting" pieces of other worlds hundreds of these relatively small pieces copied a moment in time and stuck them together smoothed out logical inconsistencies (like an ocean world abruptly ending into another world  rivers that abruptly end and then turn into another world but continues to flow).  The pcs should come from one section.  I set the game about a year after the event and people are starting to get over the initial shock and send out explores.  PCs are explorers.

All halflings are part of the same organism and share a hivemind. Kind of like a humanoid kudzu.

Hmm... All Gnomes across the world are a part of one collective nation, and consider any civilization under said nation. However no one other then the gnomes know this, not through secrecy, but through simple lack of involvement over the meilliumns. Gnomes see themselves as a kind of parent towards the other races whom are now in there 'teenage' years, giving them space to grow a develop into there own 'person', but will step in encase things start going really downhill. And/or the gnomes see the other races as a form of interest and entertainment, in seeing what they do, how far they go, and how much they mess up, before the nation of gnomes have to step in to press the big red button on all of them.

I'm assuming you want general weirdness in the world and not random effects.

Flocks of Flumphs is a good idea - make them migratory and a delicacy in some parts.
Make mimics trained as pack animals to carry and defend things in trade caravans - walking strongboxes with teeth.
Make "Magic" sentient, always listening and prone to unhelpful-helping, so any comments said aloud can cause effects (in "The Sword in the Stone", Merlin asks for his hat, and magic gives him a different hat, and he has an argument with magic in which he asks "why would I want the hat I was wearing 3 years ago? I obviously wanted my normal hat!").
(stolen from the Serpents Blood book) Make the world one of decay, where nothing lasts, and as such everything must be constantly replaced - stone crumbles, metal corrodes, trees rot and wilt as fast as they grow.
Make the world secretly a post-apocalyptic world of a cyberpunk setting, where nanobots wiped out the majority of the world but magic managed to save groups of people to rebuild after the nanobots stopped functioning. this was thousands of years ago, but every so often there will be hints that the ancient past was actually like our sci-fi future, for the players to uncover, which may delight them!

Here's a few pointers:

• Anime references, pile 'em on, never can have too many.
• Giffs, fun to roleplay, players will get a kick out of it, and there just fun to have around, plus they're pretty weird.
• Also, cater to things your players like/ think are weird.
• Reference popular culture as much as possible, I once thought of having a grung bard based off Michigan J. Frog.

This is all amazing and crazy and it's gonna really, incredibly help with the campaign, thank you all sooo much :)))

Or just read the "can you drink holy water" thread.  Lots of weirdness there.

The trope that I find myself accidentally using all the time is a magical artifact that was sealing a curse in place but was stolen.

Have an NPC who is in multiple places at once(This can just be random, it doesn't have to relate to the plot) because they can be somewhere, but they can also be somewhere else, so they're in both places at once. The NPC just doesn't realize that you can't actually be in multiple places at once. And look at the third line of my signature if this sounds weird.