It depends on which you believed in the most, or what ritual someone performed for your burial. You also see what you want to see.

We see this quote in The Lighting Thief:

I said, "What're they doing to him?"
"Special punishment from Hades," Grover guessed. "The really bad people get his personal attention as soon as they arrive. The Fur - the Kindly Ones will set up an eternal torture for him."
The thought of the Furies made me shudder. I realized I was in their home territory now. Old Mrs. Dodds would be licking her lips with anticipation.
"But if he's a preacher," I said, "and he believes in a different hell...."
Grover shrugged. "Who says he's seeing this place the way we're seeing it? Humans see what they want to see. You're very stubborn - er, persistent, that way."
_{Percy Jackson and the Olympians: The Lightning Thief, chapter 18: "Annabeth Does Obedience School"}

So we see that the preacher will see the Christian hell, while Percy and Annabeth are seeing the Greek Underworld.

We also see this with the Roman soldier in The Throne of Fire:

The ghost looked offended. "Roman, of course. Following those cursed Egyptian customs is how we all ended up here to begin with! Bad enough I got stationed in this god-forsaken oasis - as if Rome needs a whole legion to guard some date farms! Then I had the bad luck to fall ill. Told my wife on my deathbed: 'Lobelia, an old-fashioned Roman burial. None of this local nonsense.' But no! She never listened. Had to mummify me, so my ba is stuck here forever. Women! She probably moved back to Rome and died in the proper way."
[...]
Mad Claude waved his hand impatiently." Sometimes, yes. Not as much as in the old days. Their spirits sleep most of the time, now. The point is, no matter how bad a death these people had, their fate after death has been worse! All of us - all these Romans living in Egypt - got an Egyptian burial. Local customs, local priests, mummify the bodies for the next life, et cetera. We thought we were covering our bases - two religions, twice the insurance. Problem was, you foolish Egyptians didn't know what you were doing anymore! By the time we Romans came along, most of your magic knowledge was lost. But did you tell us that? No! You were happy to take our coins and do a shoddy job."
"Ah." I backed away a bit more from Mad Claude, who was now glowing quite dangerously. "Well, I'm sure the House of Life has a customer service number for that -"
"You can't go halfway with these Egyptian rituals," he grumbled. "We ended up with mummified bodies and eternal souls tethered to them, [...]
..."We couldn't go to Pluto's realm like good Romans," Mad Claude went on, "because our bodies were prepared for a different afterlife. We couldn't go to the Duat, because we weren't given the proper Egyptian rituals...
_{The Kane Chronicles: The Throne of Fire, chapter 16: "...But Not as Evil as Romans"}

So with Mad Claude we see that the way the bodies are prepared affects what happens to you after you die.

I think it all depends on what you believe in, or what your 'main' pantheon is. For example, Percy Jackson would probably go to Hades's realm, because he's Greek (as well as being a Greek demigod). Hazel Levesque would go to Pluto's realm, as she's Roman (and her father is Pluto). Jason Grace would go to Hades's realm, because he chose to be Greek. But if one of them was given an Egyptian burial, they'd go down to get their heart weighed with Osiris - maybe. This isn't exactly confirmed in the books.

This is all based on Greek/Roman/Egyptian interactions. Norse throws a bit of a wrench in the works. I don't have any source for this, but I think that if a Valkyrie took a Greek demigod, for instance, who also believed in Norse mythology, it would work.

For someone who didn't believe in anything, it looks like a Valkyrie could take them and they'd see the Hotel Valhalla like normal, or they could go to the Underworld or the Duat - but they'd see what they want to see. This would include Christian theology, and if you're an atheist, you don't get an afterlife at all, as we see in The Lighting Thief.

Finally, I seem to recall that the Mist and the Underworld are all just layers of the Duat, as seen in either The Son of Sobek, The Staff of Serapis, or The Crown of Ptolemy, but I don't have those on hand right now.