Wow. People have some impractical choices. A 50lb warhammer? Doesn't matter how awesome a warrior you are, any sustained fighting will end up with you using your bare hands.
"A viking sword with a four foot long blade that has Nordic Runes and symbols carved into the steel with a black handle and steel pommel."
Ok. so in all you'll be using a 5 foot weapon. Hope you're about 6 feet tall otherwise that's gonna be a tad unwieldy.
"Duel-wielded Fire axes"
Considering these are 2 handed at best and would be unwieldy to the point that your wrists would shatter, not to mention any swings made an that fashion would be inaccurate at best being axes, don't have the benefit of being mostly blade means any enemy could grab hold and disarm you.
"Dual katana: doesn't run out of ammo and you can throw one while you keep using the second one."
Too bad swords absolutely suck as throwing weapons mainly due to their size and the fact they aren't balanced for it. As with the above quote, duel wielding two handed weapons means you're in for more pain than you'll dish out. Weapons like wakizashi would be a better choice as their shorter blades makes them easier to use duel-wield.
"Semiautomatic pistol, and a carbon fiber machete."
The pistol is a good idea. The carbon-fiber machete is a bad one. First carbon-fiber is a bad choice for sword making because impacts are one of the things that it's not that great at. Second being made out of arbon fiber would make it too light to have much force in a swing. Anyone wearing armor wouldn't notice it.
".but if we're going all fantastical with this... flintlocks pistols. About 20 of 'em concealed in an overcoat."
Hope you have a good deal of endurance as that'd be heavy as hell. And that's just the guns, add the ammo, the powder, any replacement flints incase they break upon striking, the waddings, and of course the ramrods. More than likely you'd need more than one in case you lost one. In a prolonged battle your best friend would be the nearest chest-high wall which you'd have to hide behind for the half an hour you'd need to reload all your guns.
"A crystal battle axe with all magic elements infused to make it fatal to anything"
Make sure to have the necessary magics on it to make it both resistant to shattering from impacts and certain harmonics , but also to make such a weapon light enough to be usable to the wielder as well!
I personally would go with a bearded axe and a shield or a longsword which would be mildly decorated. Tasteful but not too flashy.