Do Aarakocra talons use STR or DEX for attack and damage? I’ve checked Monster Manual p.12 to have some clues and the higher stat for Aarakocra monster is Dex and damage is based on dex (+2) the higher Aarakocra stat.
The Aarakocra has a Str modifier of +0, and a Dex modifier of +2. As a CR 1/4 monster, it has a proficiency bonus of +2 (see the Proficiency Bonus by CR table, page 8 of the MM).
The Talon attack is the following:
Talon. Melee Weapon Attack: +4 to hit, reach 5 ft., one target. Hit: 4 (1d4 + 2) slashing damage.
So based on the calculations behind player attacks, it seems likely that this is calculated as:
Dex (+2) + proficiency (+2) = +4 to attack
Dex (+2) = +2 damage
Obviously, if you try to use Str instead of Dex, this doesn't add up.
However, it's possible that creature attack bonuses are either arbitrary or not calculated the same way as player attack bonuses are, but if this is the case there is no way to answer this question.
Somewhat disconcertingly, the Aarakocra player race from the Elemental Evil Player's Companion gains:
Talons. You are proficient with your unarmed strikes, which deal 1d4 slashing damage on a hit.
Which would be based on Str, since the Unarmed Strike is not a finesse weapon.
According to the Dungeon Master's Guide (p. 277):
When a monster has an action that requires an attack roll, its attack bonus is equal to its proficiency bonus + its Strength or Dexterity modifier. A monster usually applies its Strength modifier to melee attacks, and its Dexterity modifier to ranged attacks, although smaller monsters sometimes use Dexterity for both.
Evidently the designers decided that Aarakocra as monsters use Dexterity for both.
Aarakocra player characters (Elemental Evil Player's Companion p. 3) have no racial traits allowing them to use Dexterity rather than Strength. They would need to rely on a class trait to do so.