1. There are no rules for PCs using oversized or undersized weapons, outside of the Enlarge/Reduce spell and similar abilities that grow / shrink gear with the PC.
For the Enlarge/Reduce spell, it adds or subtracts 1d4 damage from each hit.
For Rune Knight, it adds a 1d6 damage die 1/turn to a hit.
These are bespoke rules.
2. For monsters, their exactly damage dice is flavour, and their damage output is a question of CR. However, there is advice that for oversized monsters, you increase the number of damage dice by 1 for each size category. So a reasonable number of damage dice for a Huge (2 sizes larger than medium) greatsword is 6d6, and a longbow would be 3d8.
For smaller creatures that aren't trivial foes, the damage they do with the weapon should mostly be flavour: a non-weapon based source of damage should usually be key.
...
Balance wise, extra damage is medium-strong. These are roughly even tradeoffs
+1 weapon : +1d6 damage weapon
+2 weapon : +1d12 damage weapon or +2d6
+3 weapon : +2d8 damage weapon
But a +3 weapon is legendary -- something a level 20 PC should be happy to find in a treasure horde. The ability to wield a Huge greatclub is about as good as a legendary item!
...
Practically... what would I do?
One thing I like to do is replace the "Belts of Giant Strength" with different mechanics. Instead of setting your strength, they add a Might die.
The Might die adds to Strength saving throws, Strength checks and to damage on Strength based attacks.
I might go a step further, and have the Might die be doubled if the weapon and PC are both super-sized?
For the Enlarge/Reduce spell, it adds or subtracts 1d4 damage from each hit.
For Rune Knight, it adds a 1d6 damage die 1/turn to a hit.
These are bespoke rules.
2. For monsters, their exactly damage dice is flavour, and their damage output is a question of CR. However, there is advice that for oversized monsters, you increase the number of damage dice by 1 for each size category. So a reasonable number of damage dice for a Huge (2 sizes larger than medium) greatsword is 6d6, and a longbow would be 3d8.
For smaller creatures that aren't trivial foes, the damage they do with the weapon should mostly be flavour: a non-weapon based source of damage should usually be key.
...
Balance wise, extra damage is medium-strong. These are roughly even tradeoffs
+1 weapon : +1d6 damage weapon
+2 weapon : +1d12 damage weapon or +2d6
+3 weapon : +2d8 damage weapon
But a +3 weapon is legendary -- something a level 20 PC should be happy to find in a treasure horde. The ability to wield a Huge greatclub is about as good as a legendary item!
...
Practically... what would I do?
One thing I like to do is replace the "Belts of Giant Strength" with different mechanics. Instead of setting your strength, they add a Might die.
The Might die adds to Strength saving throws, Strength checks and to damage on Strength based attacks.
I might go a step further, and have the Might die be doubled if the weapon and PC are both super-sized?