Usually melee weapons (without the finesse property) use the character's STR modifier exclusively for attack rolls and damage.

I am aware of two exceptions: The Monk (Path of the Kensei) gains the Kensei Weapons ability at Level 3 -

Kensei Weapons. Choose two types of weapons to be your kensei weapons: one melee weapon and one ranged weapon. Each of these weapons can be any simple or martial weapon that lacks the heavy and special properties. The longbow is also a valid choice. You gain proficiency with these weapons if you don't already have it. Weapons of the chosen types are monk weapons for you.

XGtE pg.34

You gain the following benefits while you are unarmed or wielding only monk weapons and you aren't wearing armor or wielding a shield:

  • You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.

PHB pg.78

And the Hexblade (Warlock) has Hex Warrior:

...you can touch one weapon that you are proficient with and that lacks the two-handed property. When you attack with that weapon, you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls.

XGtE pg.55

Are there any other ways to dump strength without limiting your melee character to finesse weapons? I'm interested in any and all solutions that use the actual weapon's stats.

For clarity Any solutions must fit the following attack structure
To hit: (d20 + STR??? Modifier + any bonuses [incl. Proficiency])
Damage: (Weapon dice + STR??? Modifier + any bonuses)

Comments/answer have highlighted to me that I was especially interested in knowing if there was a way to use an ability other than STR for weapons with damage dice of d8 and over. Extra points if you can find a published way of doing this, especially if you can hit the d10s and d12s!

  • \$\begingroup\$ Do you just want always on abilities, or would occasional abilities like Vampiric Touch count? \$\endgroup\$ – Ethan Jul 23 '18 at 15:03
  • \$\begingroup\$ Always on abilities are what I'm really interested in. \$\endgroup\$ – Isaac Reefman Jul 26 '18 at 0:47

There are two others at the moment:

Martial Arts (lvl1 monk feature)

You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons. (PHB 78)

Shillelagh (druid cantrip, works only on clubs and quarterstaves)

For the duration, you can use your spellcasting ability instead of Strength for the attack and damage rolls of melee attacks using that weapon .. (PHB 275)

  • \$\begingroup\$ I missed how many simple melee weapons are not two handed or heavy, nor already have the finesse property! \$\endgroup\$ – Isaac Reefman Jul 23 '18 at 6:55
  • \$\begingroup\$ What about >d8 weapons? Any other ways of using them? Both of these are pretty limited to low damage weapons... \$\endgroup\$ – Isaac Reefman Jul 23 '18 at 7:30
  • \$\begingroup\$ @IsaacReefman These are the only two methods I know of. Restricting them to smaller weapons might have been intentional. \$\endgroup\$ – Szega Jul 23 '18 at 7:50
  • 7
    \$\begingroup\$ @IsaacReefman I will say that restricting them to smaller weapons is almost certainly intentional (and creating Finesse weapons with higher damage dice is likely unbalanced). Dexterity-based characters are already much more powerful than Strength-based ones because of the importance of increasing armor class. At lease Strength-based attacks can deal a couple more damage on average. (This is one of the reasons why monks are among the strongest early-game) \$\endgroup\$ – David Coffron Jul 23 '18 at 9:08

To answer what you were actually interested in (d8+ weapon damage using a stat other than STR), you may be interested in obtaining a Sun Blade.

While the blade exists, this magic longsword has the finesse property

By combining the stats of a longsword with the additional finesse property it can reach a d10 dmg die when used with both hands while using DEX for attack/damage rolls.

  • 3
    \$\begingroup\$ Somewhat poetically, also the Moonblade can have finesse \$\endgroup\$ – Medix2 Jul 24 '18 at 6:34

Become a Battle Smith

(Requires playing on Eberron, or your DM allowing the Artificer class in a non-Eberron setting)

At third level Battle Smiths gain the following benefits:

  • You gain proficiency with martial weapons.

  • When you attack with a magic weapon, you can use your Intelligence modifier, instead of Strength or Dexterity modifier, for the attack and damage rolls.

--- Eberron: Rising from the Last War, p. 60

The requirement of it being a magic weapon is trivial, as you can simply use one of your infusions to make your maul, greataxe, lance, into a +1 magical weapon.

  • \$\begingroup\$ Ooh - consider a Artificer (Battle Smith) 3/Wizard X as a potentially uber Eldritch Knight? \$\endgroup\$ – Isaac Reefman Jan 14 at 21:50

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