But good point: what to do when the genres and materials literally clash! The Jedi lightsabre vs the Scorching Ray is a tricky question. I have two answers:
1) He-Man's sword would have deflected the ray as easily as a laser blast, and in their setting Jedi supposedly can do both blasters and force lightning, with the Force standing in for magic. Ergo, as the GM, I'd rule it would work.
2) However, I'm currently avoiding Star Wars because I think I've reached saturation for the franchise, and I'd disallow Jedi anyway! (possibly because I wanted so much from the series and it just isn't coming... like what the prequels could have been, or the novels, or how the canon is so crowded by going back in time and adding stories it's unrealistic, or how Darth Vader is some kind of uber messiah figure, etc, etc.)
Your point is more along the lines of a literal kitchen sink, though, as opposed to a specific setting with its own bounds that works
See? Now you're thinking with multigenre!
But seriously, we had characters that ranged from and through (covering 80 years of setting changes please realize):
a.) A Troll who proceeded to gain some semblance of taste and swagger through mental experimentation and became the dapper gentleman of the group for awhile in early games.
b.) A half-golem touring ball-player who used a magical version of Wonderboy as his weapon.
c.) A teddy bear infused with the spirit of... Gods, I can't remember who the heck it was, but who later 'retired' and became a pretty popular children's TV host.
d.) A disciple of Timothy Leary who took so many hallucinogens that he began warping spacetime through his mental gymnastics, doing impossible things (a nod to Madman from Simon R Green's The Nightside, where one specific player and I had way too much fun pulling weird pc materials)
e.) A carnival magician turned real mage when the tides began to rise up and magic came back into play from the Shadow during the Depression.
f.) A Drow who believed that blaxploitation and Chop Socky movies were literal interpretations of various cultures. He took his hair and developed a nice natural, began wearing gaudy flash clothes, and becoming a mix between the 18 Masters and Shaft/Dolemite.
They all played nice with regular Modern characters, and there wasn't an 'over the top' nature to any specific character.
Ahh, owe you an explanation: some monsters and fantasy creatures took to their new world, or began taking on various attributes. We had some Cyberscape creatures from various futuristic settings but they just don't stick out as much. Future tech came from various individuals including an Asian son of a spiritual healer and physicist who learned to pass through time and space with some mystically-manipulated physics quakery, but brought back some cool items and creations.
The WW2 plot focused around alien technology being brought back and the creation of multiple factions that brought various options into play. There were the British and their various mages from across the Empire, dustbowl hucksters a la Deadlands, the Germans creating warforged from the souls of Teutonic knights bound into armor manufactured by the Reich, and the Americans helping trapped rabbi and mystics to escape during the bombings of Dresden and leading to their own cybernetics in the field. We covered pretty much every possible mythology surrounding the various eras, and even included crossovers.
The 'new school' of mystic creatures began referring to the 'old school' elves and other denizens of Shadow as Tolkies somewhere around the 70s. It was humorous when we did get those who started out with very D&D-styled characters in Modern begin seeing the advantages/disadvantages of being D&D in Modern and changing their attitudes. To explain the whole thing in a post would be... Difficult

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Slainte,
-Loonook.