Disclaimer: The maximum theoretical answer is... as much as you want. An example being Pun-pun. Since those are not playable, this answer focuses on how getting a high Charisma without completely breaking the game.
Starting from the basics:
- Base Charisma score 18
- Leveling points +5
- Inherent bonus +5
- Venerable +3
thus a minimum of 31.
A little cheese to sweeten the deal:
- Lesser Aasimar for +2; type is Humanoid (Planetouched)
- LA+0 Magic-Blooded template (Dragon Magazine #306, p. 50) for +2; type unchanged
- LA+0 Unseelie Fey template (Dragon Compendium, p. 224) for +2; type changes to Fey
- LA+1 Draconic template (Draconomicon, p. 150) for +2; type unchanged
- LA+2 Half-Fey template (Fiend Folio, p. 90) for +4; type changes to Fey or if you prefer Obah Blessed template (Dragon Magazine #136, p.60), same bonus, type unchanged
- LA+5 Suel Lich template (Dragon #339, p. 60) for +2; type changes to Undead
- Polish with a bit of bloodline, such as the Celestial Bloodline (Unearthed Arcana, p.21), granting +1 at level 9
thus a bonus of +15.
Our type is now Fey (Planetouched), unless using Suel Lich, however taking the 1st-level feat Human Heritage (Races of Destiny, p. 152) turns it back to Humanoid (Human, Planetouched). It requires us to be of a half-human or human-descended race, I expect Lesser Aasimar to qualify, otherwise, what's the non-Aasimar part?
I prefer cheese with my cheese:
- The Worm of Minauros magical location (Fiendish Codex II, p. 49), for +1 unnamed bonus; to be renewed every 30 days by committing an act of obeisance (if non-lawful) or a corrupt act (if non-evil)
- A Pact with the Devil (Fiendish Codex II, p. 23), for +1 unnamed bonus; it tends to lead one toward damnation
thus another +2.
Picking the right classes:
- A single level in the Dragon Devotee class (Races of the Dragon, p. 84), for an unnamed +2.
- A single level in the Anointed Knight class (Book of Exalted Deeds, p. 49), for the Divine Clarity oil and an unnamed +1.
- A single level in the Half-Water Elemental class for a racial +2 (Dragon #326, p. 89)
- Two levels in the Half-Air Elemental class for a racial +2 (Dragon #326, p. 87)
- Three level in the Half-Fire Elemental class for a racial +2 (Dragon #326, p. 88)
- Four levels in the Ghost savage progression (http://archive.wizards.com/default.asp?x=dnd/sp/20040117a) for an unnamed +4.
- Six levels in the Warchief class (Miniatures' Handbook, p. 24), for an unnamed +6.
- Eight levels in the Doomlord class (Planar Handbook variant, p. 47) for an unnamed +2.
thus another +21.
Picking the right feats:
- Ability Enhancer (Dragon Compendium, p. 91), enhances the ability bonus of any Transmutation spell by another +2.
Picking the right spells:
- From Zachiel's list, the Paladin's spell Righteous Aura [Abjuration] (Spell Compendium, p. 177) for +4 sacred bonus to Charisma; to be persisted.
- The Bard's spell Snowsong [Enchantment] (Frostburn, p. 105), for +4 Morale bonus to Charisma; to be persisted.
- The Cleric's spell Visage of the Deity, Greater [Transmutation] (Spell Compendium, p. 231), for +4 unnamed bonus to Charisma (if Good); to be persisted.
- The Bard's spell Nixie's Grace [Transmutation] (Spell Compendium, p. 148), for +8 enhancement bonus to Charisma; to be persisted.
thus another +20, or +24 with the Ability Enhancer feat.
For persisting Bard spells, Divine Metamagic does not work; an Incantatrix (Player's Guide to Faerûn, p. 61) can, however, persist spells either through Cooperative Metamagic (2nd-level) or Metamagic effect (3rd-level).
Buying the right items:
- The Command armor property (Defenders of the Faith, p. 23), for a +4 Competence bonus to Charisma.
thus another +4.
Knowing the wrong persons:
- A Lilitu's Gift (Fiendish Codex I, p. 43), for +2 Profane bonus to Charisma, to be renewed every 24 hours. Makes alignment drifts toward Chaotic, perfect to balance the Worm of Minauros!
thus another +2.
For now, that's a grand total of 99.
Of course, how to manage a deal to get all those is an exercise for the reader... A Cleric/Sublime Chord/Eldrich Master with the Alternative Source Spell feat could get most of it I'm told, which would most probably be foregoing a few of the suggested classes (starting with the Doomlord).
Among other things, I picked ideas from Ways to increase Charisma?, which includes some builds and The most cost effective way of boosting charisma? and I have not read them fully.