A Hunter Ranger (11), Oathbreaker Paladin (7), Barbarian (1), Hexblade Warlock (1) can deal at most 3126 damage without relying on any dice rolls or legendary magic items.
A lot of this relies on the unusual Hunter Ranger's Whilrwind Attack feature which states:
You can use your action to make a melee attack against any number of creatures within 5 feet of you, with a separate attack roll for each target.
In the Sage Advice Compendium the following has been stated:
Whirlwind Attack is unusual, in that it’s a single attack with multiple attack rolls.
I have asked the OP if this feature could be used following the ruling in the Compendium, to which they said that it could.
To absolutely maximize our damage with this attack we would want to hit as many creatures as possible. We could surround ourself in tiny creatures, and as there are 26 squares within 5 feet of us and tiny creatures take up one fourth of a square, we could have up to 26*4 creatures all within 5 feet of us.
Thus, most of our static damage will be applying 104 times over.
We would want to be using a +3 magic weapon to gain +3 to each damage roll.
We would want to be raging which states:
When you make a melee weapon attack using Strength, you gain a +2 bonus to the damage roll...
We would want to have our Aura of Hate active which states:
Starting at 7th level, the paladin, [...] gains a bonus to melee weapon damage rolls equal to the paladin's Charisma modifier...
We would want to be using the Great Weapon Master feat which states:
Before you make a melee attack with a heavy weapon with which you are proficient, you can choose to take a -5 penalty to the attack roll. If you do so and the attack hits, it deals +10 damage.
And we would want to be under the effects of shapechange and be turned into a Pit Fiend (It has a +8 to Strength and a +7 to Charisma and its CR is less than 21 so it is a valid creature for these spells).
The Pit Fiend already uses a mace for one of its attacks so I see no reason it could not also use a +3 mace that you happened to have on you at the time.
We would also be able to use all of these features even while shapechanged because the spell states:
You retain the benefit of any features from your class, race, or other source and can use them, provided that your new form is physically capable of doing so...
Thus the bonuses to damage that would be applying to every creature in range would be:
+2 from Rage.
+3 from a magic mace.
+8 from our Strength modifier.
+7 from our Charisma modifier with out Aura of Hate.
+10 from the Great Weapon Master feat.
This gives us a total of 30 damage against each of the 104 creatures, so we already deal 3120 damage. However, we can improve this slightly by adding in the Hexblade's Curse option, dealing 6 more damage to a single cursed creature thus increasing our total damage to 3126.
A lot of this strategy can be used every single turn as there is no limit on the uses of Whirlwind Attack and the Aura of Hate is a passive effect that will always be on. Unfortunately we would only have two rages (though they do last 1 minute) and one use of the Hexblade's Curse per day.
Even if we only hit a more reasonable number of creatures, say 3, we didn't use Hexblade's curse and we weren't raging we would still be dealing 84 static damage, which is certainly a respectable amount.
If we are allowed to use a Belt of Storm Giant Strength we would be able to deal even more damage.
We could shapechange instead into Titivilus who has a +8 modifier to Charisma and wearing the belt our Strength modifier would be +9. These changes would increase our maximum damage to 3334 without any dice being involved at all.
This would change our non-raging, non-cursing, three-target-only attack's static damage to 96 damage.
Theoretically another way to increase this damage is to become tiny ourselves but I do not know a way to make a medium creature tiny, if there were one then we could have three additional tiny creatures in our square and thus within 5 feet of us allowing them to be targets of Whirlwind Attack.
This would increase our maximum non-dice-related damage to 3216 and combining this with the above strategy using legendary items would increase this to 3430 damage.