Well, first you likely want to identify what exactly those concepts are (sorry, while I'm aware of them, I've never watched the shows you refer to so I don't know what they are).
A common theme is the guy or gal who gets beaten down only to rise to their feet even more powerful than before. This applies to both good guys and bad, but generally only important characters. For example, you might want to use the optional Second Wind mechanic from the DMG and maybe even throw in some kind of temporary buff on top of it (but only allow it to be activated when the character is in a desperate situation). I would recommend not making the buff too complex, as it could be challenging to recall the particulars during combat - I'd recommend something straight-forward like advantage and/or a bonus to damage equal to the character's level.
You might allow characters to jump down from great distances without injury (falling should still hurt). You could also increase horizontal and vertical jumping distances.
Those are just examples though. First and foremost is identifying what concepts you want to bring in (maybe it's not the power aspects at all, but rather the quirky characters in which case you'd want to work on creating a roster of oddball NPCs and encourage the players to do the same with their PCs).