I asked on the D&D beyond discord, got an answer that is how I would have ruled it, but then stumbled into more confusing rules and 'clarifications' that brought my thought into doubt again.  Please read this all before responding with how you would rule at your table and what rules support how you would rule it if you can find any:

So Rabbit hole scenario.  I was thinking of how attacks can have multiple damage types.  Scenario:

Lets say someone is attacking with a flame tongue long sword, and has arcane weapon cast on it tuned to thunder, while using divine smite for the radiant damage.

So damage is mostly easy, 1d8 slashing + 2d6 fire + 1d6 thunder +2d8 radiant + str (assuming they are using str).  Where in the rules can i find guide for the type of damage the str is so resistance can be factored properly?

Lets add in hunters mark spell and Sneak attack:
Hunters Mark: You choose a creature you can see within range and mystically mark it as your quarry. Until the spell ends, you deal an extra 1d6 damage to the target whenever you hit it with a weapon attack

Sneak Attack
Beginning at 1st level, you know how to strike subtly and exploit a foe’s distraction. Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.

What is the damage type on those?

So what we have, as written, is: 1d8s + 2d6f + 1d6t + 2d8r + str? + 1d6? + 1d6?

Lets imagine some sort of undead demon thing, vulnerable to radiant, resistant to fire, immune to slashing.  Nothing in the rules tells us the damage type of the last bits, and everyone has assumed, likely due to past editions, it would all be slashing.  What we do know is that *all* of these sources add to the weapon damage, and thus the the weapon attack.  We know this because of how crits work, and that all these sources say "attack does an extra ___ damage" thus it adds to the attack pre crit rather than post crit.  So lets ignore the assumption that all the extra damage is slashing, and look at possibilities.

1) First, It could be slashing every time.  I mean its a possibility, and would mean that all those bonuses are jsut ignored.
2) you might get to pick which type from what the attack has.  So the str/1d6/1d6 could be your choice of slashing, fire, thunder, radiant. You pick radiant once you have figured out that's what it doesnt like, and boom, all those number are worth double (and some quadruple on crits)
3) its untyped damage, the the blood loss of a stirge bite.  This would mean, that unless a creature has resistance to all damage, or immunity to all damage, you'll do the full str+1d6+1d6 even if it was immune to every damage type separately.
4) what caused the rabbit hole, it might not matter due to order of operations:  If you look up resistance, vulnerability, and immunity, you apply after damage is calculated.  The example only lists and attack of one type, and there has been no errata nor Jeremy Crawford rulings on it, but reading it, you roll damage for the attack, apply and + or - to the damage (like say, if you have armor that subtracts 3 from all damage taken, you apply that here) then apply resistance/vulnerability/immunity.  So you might just "roll damage" then say "yep it has resistance, vulnerability so those cancel, and it doesn't matter cause immune"

to make this more confusing JC (Jeremy Crawford, 5e game designer) has said three things about all this, all damage is typed (even tho there is actually examples in the Monsters Manuel of typeless damage), sneak attack being slashing on a flame tongue, and hunters mark being "any type from the attack."  So he has actually supported and refuted 1, 2 and 3 directly.

so, with all of this said, what do you think?  If you swung a sword that cleaved into the flesh of a monster, burning it with fire, shattering bones with sound, and smiting with the grace of a god, in the back, with all of your might, how should it be handled.  If its immune to slashing, is it now immune to everything else?  if it was vulnerable to slashing, but immune to fire, should it still be immune to it all of it?  does it take damage just because you hit a vital organ even though it takes no damage from any typed damage?

I was just going to say "I think sneak attack and damage modifiers are meant to be slashing," but stormknight goes all the extra miles.

I get that, but Hunter's mark which works exactly like sneak attack got this from him:

https://twitter.com/JeremyECrawford/status/808824943299264512

When you attack with a flame tongue, the attack, including crits, does Slashing and Fire.  Again this gets into why i said and i quote: "JC (Jeremy Crawford, 5e game designer) has said three things about all this, all damage is typed (even tho there is actually examples in the Monsters Manuel of typeless damage), sneak attack being slashing on a flame tongue, and hunters mark being "any type from the attack."

In the thread about hunters mark he directly does contradict himself, at first saying its any, then saying its only the base.  In sage Advice he said all damage in the game is typed, even tho you can find examples of un-typed damage, like the Stirge.  We know hunters Mark and Sneak Attack mechanically work the same when it comes to their damage (even if how you trigger that damage isn't mechanically the same).  So he has said, that when making an attack, bonus un-typed damage has to be typed.  Hunters mark, you get to pick from any damage type of said attack, sneak attack you use the base weapon.  So do we need to go case by case, or assume he isn't sure himself?  The general rule of 5e is keep it simple, so case by case is out, and we have also found a few instances in the MM of untyped damage, so we also know that he may not be right about there being no such thing as un-typed damage.

This is why I was asking for the supporting rules, as I had already pointed out JC isn't a "reliable narrator" in this case.  I know how I would personally rule, but that doesn't really help when people are asking what the damage type of +str is universally.  Even in that twitter thread, you can see someone saying they thought sneak attack was un-typed.  So its not exactly clear in the rules.  I thought it was, I thought all along that bonus damage was the base weapon, due to me playing all the past editions, and that's how those worked.  Then about a year ago, I saw the hunters mark clarification and was like "oh I guess you get to pick, cool."  Then recently someone asked me what the damage type of the +str was in their attack.  As I like to look things up and explaining weird rule interactions, I found the ruling on sneak attack that was in opposition to the ruling on hunters mark.  And thus before I answer, now knowing JC doesn't have a definitive answer on this, I am back to checking errata, sage advice, and rules (especially stuff that has come out since 2016) for answers I can point to.  At my table, I use base weapon, as that is how past editions did it, but I don't like teaching home rules to people that are asking me questions.

Anyway the best "rule for it" I have found is, well roll20 applies it as the base weapon damage, but then i remembered, roll20 is also nothing official.

I would rule that any non-magic damage bonuses are the weapon's damage type, but that's just me. My reason being, if you're super strong, you can slash with your longsword even harder. If you're super sneaky, you can stab with your dagger in the enemy's weakest point, so the piercing damage of the weapon is that much more effective. 

Any other damage types from magical effects would just simply stack on top. 

I think the problem here is that you're trying to treat all damage rolls with multiple damage types as the same without distinguishing between the damage the attack would normally do and any extra sources of damage, and also kind of ignoring the nuances between different damage bonuses.

When a rule says "the attack deals an extra X damage" or "you add X to the damage" that's generally referring to the original damage of the attack before you started piling on exceptions that introduce more damage types the attack wouldn't normally have. For instance, it's not too hard to see from context that the text about adding your ability modifier to the damage roll of weapon attacks is referring to the damage of the weapon.

From that perspective, Jeremy's tweets on Hunter's Mark make sense; if you're smacking someone with a weapon, use the weapon's damage type. Likewise, a Sneak Attack with a Flame Tongue rapier is still a Sneak Attack with a rapier; the bonus from the Flame Tongue's effect or a spell like Elemental Weapon is separate from the damage a rapier naturally does. If the melee weapon attack that triggered it is something unconventional, like a vampire's unarmed strike which naturally deals both bludgeoning and necrotic damage, choose either one.

A stirge isn't an example of untyped damage. Its blood suck causes the target to lose HP, completely bypassing any rules related to taking or dealing damage. When the rules give you a damage bonus, it's always going to end up being applied to some source of damage like a weapon or a spell that does in fact have a type tied to its damage.

Also, the case presented with multiple types of damage from smite, hunter's mark, sneak attack, etc...

You'd have to be multiclassed into Paladin, Rogue, and Ranger to pull that off. Meaning your character would need STR, DEX, WIS, and CHA all above 13 to do it, which is pretty much impossible by standard array or point-buy. So it's an extreme min/max case only possible if you roll incredibly overpowered stats and spend at least five levels (2 paladin, 2 ranger, 1 rogue) to build that up. NOTE: you'd also have to attack with a melee finesse weapon to get sneak attack, so a flametongue longsword is out...

But again, I concur with the previous statements. The STR (or DEX) modifier, sneak attack, and hunter's mark adds to the weapon's base damage type of slashing, piercing, or bludgeoning depending on the weapon used. Then the magical damages stack on top of that.

Quote from Maestrino >>

Also, the case presented with multiple types of damage from smite, hunter's mark, sneak attack, etc...

You'd have to be multiclassed into Paladin, Rogue, and Ranger to pull that off. Meaning your character would need STR, DEX, WIS, and CHA all above 13 to do it, which is pretty much impossible by standard array or point-buy. So it's an extreme min/max case only possible if you roll incredibly overpowered stats and spend at least five levels (2 paladin, 2 ranger, 1 rogue) to build that up. NOTE: you'd also have to attack with a melee finesse weapon to get sneak attack, so a flametongue longsword is out...

But again, I concur with the previous statements. The STR (or DEX) modifier, sneak attack, and hunter's mark adds to the weapon's base damage type of slashing, piercing, or bludgeoning depending on the weapon used. Then the magical damages stack on top of that.

 

 Vengeance Paladin gets hunters mark, so you'd just need to go rogue/pally

Each damage type must/should be typed due to resistances and immunities. In the given example Fire is Fire, Divine Smite is Radiant, Lightning is Lightning, Everything else would be piercing from a Short Sword or Rapier. Sneak Attack would be piercing because you used a piercing weapon to poke the bad guy in the kidneys (or whatever). Hunter's Mark makes your strike hit harder, it's not going to magically change a pierce into a bludgeon.

Ah, I missed the Vengeance Pally. Still, you'd need three scores at 13 or better to hit that multi-class, which is theoretically possible with point-buy. Definitely a min/max build.