The most bewildering one was on Ye Olde Guilde (the previous version of this forum) when I was running one of the many, [i]many[/i] incarnations of my GEARs RP. GEARs is a sci-fi RP set solely on one world, with a fairly detailed setting that has various mysteries to it. The tech of the setting is quite explicitly detailed too. It features smallish mecha (the titular GEARs), a bit bigger than powered armour, but much smaller than your regular giant robot. The people in the setting are all anthro animals too, which is also an intrinsic part of the setting and plot. 

Anyway, the game was in Casual, but it could have easily sat in Advanced, IMHO. Someone submitted a character app, and they clearly hadn't read [i]anything[/i] about the setting or RP at all. 
They had made up a vulpine character who was from 'another planet than Landren' - Landren being a [i]country[/i] in the setting, not a planet. Let alone space travel not even being a thing at all. 
Their mecha had 'laser particles'... (in it's legs!) I don't even know [i]what[/i] that means, let alone the fact that energy weapons were experimental tech in the setting and not readily available to the players. It had a bunch of other nonsensical things too, but I remember that being the standout one because of the odd wording.
The whole app read like it was written by a little kid. 
I rejected it as it clearly didn't fit anything, but I made sure to do so politely. I was still completely bewildered by it, and we did used to joke about 'space fox' afterwards in the RP group. 

There was also a dude who joined the same RP or another version of it, who [i][b]clearly[/b][/i] was just there to get his rocks off with furry smut RP - or at least, to try to. He had no knowledge or interest whatsoever in the setting or anything about it, and was just constantly trying - very, very poorly - to hit on every character that was there. I remember this specifically, because he offered to be someone's co-pilot, and when asked to do something in character, he replied his character had no idea what that meant... not sure how they'd have ended up in a hi-tech war machine if that was the case.
He also tried to start a 1x1 with me, and his characters were as deep as a dry puddle, and he had no interest in discussion about setting, story, or anything. All his characters did was just keep 'looking at' mine with no elaboration. 
That was just eye-roll worthy. 

Otherwise, I had a friend who was a dyed-in-the-wool weeb when we were teenagers, and first getting into TTRPG's. 
We had just started out on our journey into playing TTRPGs, and a slightly older friend was running a high fantasy RPG for us - it was from an old paperback book called 'Dragon Warriors'. Tolkienesque high fantasy stereotypes through and through. Simple system, great for a beginning point for anyone new to RPGs. 
Me and my other friends were all playing fairly familiar - if a little childish - high fantasy characters. We all knew the style and the tropes, and were playing to the setting. 
Weeb friend, well... 
He was basically using anime stereotype jokes all the time. Describing his character having anime sweat drops, giant jiggly boobs, fireballing people for disagreeing or upsetting her (as if it was a cartoon and they just shrugged it off like Wile-E-Coyote), and so on. 
Needless to say, everyone got very fed up with this, and the GM eventually had to say that their character did not fit at all with the others, and to tone it down. They got pretty huffy about this and didn't understand the issue. 

They had their own OC too, and talking about that RP makes me remember him. He was an absolute Mary Sue; half vampire, half demon, and cribbed looks, powers, gear and everything else from basically anything and everything you can think of. Adamantium (or equivalent) skeleton, giant sword(s) that were supernatural, Super handsome (apparently; they basically looked like Vincent Valentine and Sephiroth's lovechild) but brooding, all the girls love him, but he's just too cool and angsty to show his super deep feelings. A plethora of magical abilities (naturally) a spaceship that would make the SDF-1 Macross look puny (oh, and it was full of his own Space Marine chapter, and crewed by a mixed assortment of anime babes from various franchises who all lurrrrvvve him) A bad boy because 'heroes are too goody-goody'. All the personality of a small radish and so overpowered that nothing at all feasible was a challenge to him and his 'weaknesses' weren't really weaknesses of any relevance. 
Typical teenage power fantasy, I know; but even now any time I see some overpowered OC on DeviantArt or somewhere it makes me smirk as I remember the excesses of my friend's character. 

Not that I don't have my own characters who had silly moments, especially when I was younger. But I always think they've been much more restrained by comparison.