To what extent are weird 3rd party books allowed in this? I've got a few...
The Ceptu race in Oathbound: Realms of the Forge can use int for their attack and damage rolls with melee weapons instead of strength, though can use charisma with weapon finesse. (they use a weird extremely simple telekinesis and thus hold melee weapons with their mind). I have to talk about this book whenever I get a chance because anything that considers a race of giant floating telekinetic jellyfish to be a normal player race (listed under the races chapter, only has +1 la, etc...) needs more love then its getting. There is also a pathfinder edition of this book, so the race can be added to that list as well.
In the Warcraft Rpg - Horde Guide there is a pair of feats for undead: Mind Over Matter allows undead to add their charisma to their hit points in place of constitution, and a sequel feat named Mental Stamina lets them use charisma for everything that they would normally use con, including fort saves, barbarian rages, breath weapon dcs, etc.
In the D20 modern rpg, the Int hero base class can add their int to attack rolls in place of strength or dex against one opponent for the rest of combat if they make a dc 15 int check (minimum possible level to get this is 3) and the feild scientist presteige class can, at first level, add their int bonus to ac, though they loose it if they would be denied dexterity.
The most questionable set of sources I have is the varied "Complete" guides that Goodman Games have produced; with rules like "drow liches have d20 hit dice" and "beholders get along quite well, building empires of 800 different specialty beholders to take over the world with" so of all my sources these are the ones that shouldn't be included in probably any list, but in their guide to fey they have a series of races and classes intended to be made into any basic fey from like the monster manual. To this end, there are a couple of feats (can only be taken by fey) meant to replicate the abilities of like nymphs and stuff; Unearthly Grace adds their charisma as a bonus to all saves, while Unearthly Luck grants it as a bonus to armor class.
This is just a "abilities I remember off the top of my head" list, but I can do a thourough search of my sources if theres any interest in this at all; I'm sure this list will be more useful and fun to produce then my last couple lists, which include "all outsiders ranked by challenge rating" and "every advanced material for armor/weapons" (both of which are a little outdated at the moment, but I could upload if anyone wanted them and could tell me where would be a good place to do such a thing.)
Edit: I don't have access to my copy of Oathbound at the moment and I only have the srd for the d20 rulebooks so I don't have page numbers for those. The ones regarding undead and charisma are in the Horde Player's Guide, both on page 34; and even though I shouldn't be acknowledging its existence the last ones I mentioned (the ones for fey) are page 45 in The Complete Guide to Fey.
Also, Masters of the Wild, a proper, not 3rd party dnd book has a variant on page 18 for letting barbarians use strength on intimidate checks.