"Inclusive or" doesn't specifically mean "saying yes when someone asks an X or Y question".
Inclusive or is the general function that takes X and Y as inputs and returns true if either one of of X or Y is true. Which is in contrast to an exclusive or, which returns true if exactly one of X or Y is true, but not both. So the joke is "you expected this to be an exclusive choice between two options, but I interpreted it as an inclusive or and said yes, indicating that one or the other is true but without telling you which one".
If the answer is "no" to an inclusive or, then neither X nor Y is true: which cashes out to normality. Like "Do you want tea or coffee? -- No" means you want neither tea nor coffee. Whereas if the answer is "no" to an exclusive or, then it could be the same case where neither X nor Y is true, but it could also be because they're both true. So "Do you want tea xor coffee -- No" would be ambiguous between "I don't want either" and "I want tea AND coffee".
Other memes might present some fictional dialogue as setup and context before the image or final line or quote or whatever at the bottom delivers a punchline.
"Nobody: " could be read as "Nobody said nothing". Sometimes further exaggerated with extra lines of hyperbole about how absolutely nobody said a single goddamn thing.
Which, in theory, serves to emphasise that the punchline comes out of left field. An absurd non sequitur with no setup, no context, and no-one asking for it. It's not a response to anything, it's just an inexplicable bit of nonsense that came out of nowhere.
But also it's really easy to tack that on to just about anything that would otherwise have just been a mildy funny image, in a lame attempt to heighten the comedy of it. So it gets overused.