Do I have the right to have my character "blast off at the speed of light" as a reference to Pokemon's Team Rocket Trio?
Do I have the right to have my character lock another character in an office room, calling this the "Serious Punishment in the Serious Room", as a reference to The Stanley Parable?
Do I have the right to quote The Simpsons' "A Boozehound Named Barney" lyrics, adapting them to my characters, essentially doing with my characters what this DeviantArt submission did with MLP characters?
Do I have the right to pay a homage to Full Metal Jacket by having my character join a fictious army, then chuckle at the drill instructor's theatrically intimidating behavior, then, when the drill instructor asks him
Do you think I'm cute, Private my character's name? Do you think I'm funny?
make him respond to the drill instructor "Actually, yes" - then have the drill instructor gut-punch my character and yell:
You little scumbag! I got your name! I got your ass! You will not laugh! You will not cry! You will learn by the numbers! I will teach you! Now get up! Get on your feet! You had best unfuck yourself, or I will unscrew your head and shit down your neck!
Do I have the right to do other things of this kind?
I used to think I did. I thought I had the right to quote other works, as long as the size of the quote is insignificant in comparison to the size of the quoted work AND to the size of my work, for reference or for parody. Especially since I can see mainstream works do this too, for example this MLP's allusion to Splinter Cell - The allusion in this case seems clear enough to the fanbase.
What makes me doubt if the above reasoning is correct is the Edgar David's won lawsuit against Riot Games. While David's public image is not a work of fiction, I would suppose that the right of parody or reference still applies. Apparently, this is not the case.
What is the situation in the EU? What is the situation in the USA? Should I split my question into two questions, one asking about EU and the other one about USA?