So, hundreds of [INSERT MONSTER NAME HERE] are treating a peaceful village? And your party is like "Yep, let's go head-to-head and defend the people"... I hope you have tons of minis or The Lord of the Rings game lying around. Also, a Deus-Ex Machina pre-planned in case your balance calculations are way off.
There is a way to simplify things without breaking or changing the balance. Let's say 50 goblins are walking your way, goblins have 7 HP on average. If your characters gained a few levels, they will be killing those boys in 1 or 2 hits 95% of the time. So, if the goblin takes 4 damage - he isn't killed. But instead of writing in a notepad that he has 3 HP left I just mark him as injured - put some plastic circles from used water bottles onto him - the filthy way of Mat Mercer. Now, if the injured goblin takes another hit, he is done.
Obviously, sometimes a goblin could take 3 damage and then 2 more, and die, while he should have had 2 HP left. But this is just too rare when players are of a sufficient level.
There may be a swarm of enemies, approaching, like a wave. Maybe not enough miniatures in your bag. They are climbing on top of each other, definitely closer than 5 feet apart. In this case, tracking individual monsters is not an option. I would mark cells, currently occupied by those enemies (with tokens or marker). Have a total enemy HP pool, let us say 500 HP. One cell is still one monster but if the player deals not enough damage to kill it outright, I assume that on the next turn a different enemy takes place of the old one and change nothing on the board. I subtract that damage from the general pool and go on. If damage does kill the enemy, I mark the cell as cleared and the player can move there if he wants to.
Unless the bodies of an enemy disintegrate, they could form difficult terrain or even walls after a sufficient amount has been laid to rest on a given cell. A marker would be of use in that case.
Every rule here is situational, for regular combat my game is very much Vanilla.
Cut in half
There is a Cleave optional rule in DM Guide. I like to combine it with the rule above (about tracking XP). But players can only Cleave weak minions.
If you deal 14 damage with a spear and another goblin behind the one you killed, then you impale both of them. If you end someone with a short sword and another one next to him, you can take a few more heads. A Warlock may want to find a nice line of fools to blast while a rogue gets himself in the middle of the crowd before starting his dance of death.
I add one modification: You need to deal enemy's Max Hp worth of damage to him to cut through him and hit the next one. So if there are 2 goblins and you deal 20 damage, you kill exactly 2 of them and it doesn't matter if they were already injured - makes it easy to calculate, just divide Damage by HP. Usually, there will be leftover damage that can only injure the last minion - for him, I roll a Dexterity saving throw and he becomes injured upon failing.
For Piercing Damage the DC is 10
For Slashing/Radial Damage DC is 20
For All other Damage the DC us 15
I didn't want to complicate things but also wanted a way to reflect the fact that a Dwarf who is spinning with a large hammer will cause many broken bones and screams of pain. Meaning he has a higher chance to just injure someone.
While someone with a dagger or a bow is likely to go for fatal strikes - a Rogue would rather fully concentrate on stabbing a couple of neck arteries rather than delivering one more belly cut.
A few limitations worth mentioning:
Damage can carry over only if the next creature has the same or lower CR rating, AC and conditions (Advantage/Disadvantage). This way killing a goblin wouldn't allow you to damage their boss.
Damage can only spill in one direction from the defeated creature (clockwise or counter-clockwise or in a line from nearest, based on an attack-type) and can't skip. If someone has two daggers or swords, they can negate this rule.
Combat is not Fencing
A juicy fight needs your full concentration on the Epicness, so it is important to know that all the rules are there to provide a representation of probabilities rather than a direct conversion of Actions into mechanics. For Example:
"Barbarian is making an attack with his Axe." - this doesn't necessarily mean that he is doing the same old Axe swing every time. Maybe Goblin is focused on the weapon while the barbarian bites off Goblin ear with his mouth. And then punches another Goblin's ribs with a shield. Or In a bar fight: 4 unarmed damage doesn't have to immediately mean a punch to a face. Maybe the character simply points at the nearby table where the other player's Bard is romancing the opponent's mother. That is 4 points of Moral damage... yes, in the interest of rules it is still physical and not psychic damage... unless DM makes a ruling...
The damage of any weapon is provided to represent an average output someone would have with it. And while your character may be an expert swordsman - you yourself don't have to be. It is implied that your fighter decides based on the situation when to Lunge, Remise, Parry, Passata Sotto or kick someone in the nuts while you just roll an Attack action.
Also: A good warrior wouldn't miss when given an opportunity to deal a fatal blow. So when Attack action fails, it could also mean that there was no opportunity to perform a hit and the warrior didn't swing his sword at all. If he hits and deals 2 damage it could mean that he just pushes the enemy with his shield to throw them off-balance.
Also, you can call it heresy, but: When a fighter makes 4 attacks during his Action, it can also mean that he is doing a very strong one that has 4-times the damage than he could 20 Levels earlier (Yes, I know he rolls for each one, but it just means that he is much less likely to totally miss during his turn. Because he is very strong).
Now if there were (probably is) a Role-Play system with all the things mentioned above being performed with their own special rules, that would also imply that unless you are using that rule, you are not performing any interesting actions and just doing traditional combat, but that would be a very boring Barbarian or Bard...
As a DM I don't talk about this stuff directly, but every now and then try to show that if something makes more sense in the given situation and doesn't affect the numbers, it is what is happening.
Epic encounter balance
Does cutting through break the balance and should you account for it? Obviously, depends on how critical balance and XP are to your enjoyment of the game. And how powerful the characters should feel in your story. Too much power and you may lose some of the tension. I can offer a few counters to swing the balance back into the goblin's side a bit. But I personally feel fine playing without them:
If a player is surrounded, the enemies get +2/+5 to hit instead of Advantage. That would be +2 if 2 enemies are on opposite sides and +5 if 3 are attacking one player from relatively different sides. Advantage may seem better (for the one getting it), but if enemies have Pack Tactics or any other Advantage source, you'll get benefits stacked and players overwhelmed. Also, in our campaign encounters often end with everyone surrounding the boss who has his abilities lowered by spells, and while everyone realizes there is no reason to wait for the previous player to finish his turn before rolling your own attack, DM is playing this:
Anything else you can do?
Yes, here is a list of ingredients to spice up your encounter:
High ground/Tight passages - players would welcome any opportunity to ration the flow of enemies, create choke points.
Civilians/Structures - if the environment demands things to be protected or destroyed, the opponents themselves are no longer the main point, which is a great thing. You can say that the flow of zombies isn't meant to be defeated, but stopped or held back for long enough for the people to evacuate.
A Boss - Yeah, the only thing more intimidating than a swarm is a queen in charge of it.
Timer - Holding the line until the mage arrives with a backup or blasting forward to stop the doom mechanism, instantly scales the epic-ness of a horde slashing exercise.
Decision - It is infinitely better when a fight starts with the player's choice to start it, instead of DM's "Surprise, we'll be throwing lots of dice today."