Can you apply multiple on-hit effects and if you can, who decides the order they're applied in?

Question

I'm thinking of making a character who is multiclassed into both Pact of the Blade Warlock as well as Arcane Archer that uses a bow as their pact weapon.

If you apply the warlock invocation Eldritch Smite which deals additional damage when you hit and knocks a target prone, can you then also apply an Arcane Shot to the target?
And if this is the case, who decides the order? Or do the effects and results happen simultaneously?

This may matter if, for example, the target is flying and then knocked prone via Eldritch smite, but you also choose to use a Bursting Arrow to affect the targets around it; does it affect the targets around it after it falls from being knocked prone (assuming it cannot hover), or before it is knocked prone?

Another (theoretical) example: Say there is an on-hit effect that restrains a creature, which would then give it disadvantage on Dexterity saving throws. If you use it simultaneously with an on-hit effect that forces a Dexterity saving throw, would the creature have disadvantage on the save, or would that not have applied yet?

Answer 1

First off: Yes, you can apply both effects on a single hit.

Neither Eldritch Smite nor Arcane Shot require an action, reaction, or bonus action. They are simply abilities that you, the player, have the option of activating upon a successful weapon hit. Nothing in the DMG or PHB prohibits the activation of multiple "free" abilities at the same time. Therefore, there should be no problem using them both in one round, on the same attack.

Secondly, the player controlling the character (i.e. you) gets to decide what order the events happen in.

One of the posts V2Blast linked mentions a very helpful (although technically optional) rule from Xanathar's Guide to Everything (p. 77) regarding simultaneous effects:

In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table - whether player or DM - who controls that creature decides the order in which those things happen.

In this case, the Attack action is happening on your turn. That means you get to resolve the simultaneous effects, which both take place "when you hit with an attack". Interestingly enough, this rule implies that if you were to somehow make this attack as a reaction on the monster's turn (e.g. by readying it), the monster would get to choose what order the effects resolve in instead.

So in the case of our theoretical, it would be the attacker choosing the order in which the effects resolve, assuming the attack is made on their turn. Most likely, they would want to impose disadvantage first, then force the save.

Answer 2

You decide the order

Xanathar's Guide to Everything, pg. 77 gives guidance on adjudicating situations when things are happening simultaneously:

Simultaneous Effects

Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature’s turn. If two or more things happen at the same time on a character or monster’s turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character’s turn, the player decides which of the two effects happens first.

It gives the player whose turn it is advantage, and ensures more fun, because it favors the current player.