No, you can't choose the same ability score twice. Here's why:
The intention is usually in the wording - in this case, this,
and two other ability scores of your choice
to me this means you need to choose two ability scores other than Charisma.
A variant human's starting feat and extra skill proficiency are racial traits, and are lost when reincarnated into another race.
The reincarnate spell description states, in part:
The reincarnated creature recalls its former life and experiences. It retains the capabilities it had in its original form, except it exchanges its original race for the new one and changes its racial traits accordingly.
The variant human's racial traits are listed as:
[...] your Dungeon Master might allow these variant traits, all of which replace the human’s Ability Score Increase trait.
Ability Score Increase. Two different ability scores of your choice increase by 1.
Skills. You gain proficiency in one skill of your choice.
Feat. You gain one feat of your choice.
These traits - along with the other base human traits - are all replaced by those of the new race.
The same is true of half-elves, who get the Skill Versatility trait:
You gain proficiency in two skills of your choice.
If the half-elf is then affected by reincarnate, they will lose these two skill proficiencies. The skill proficiencies come from a trait granted to the character by their race.
This question is not officially addressed in the Sage Advice Compendium, but 5e rules designer Jeremy Crawford unofficially confirms this interpretation on Twitter:
If a human is reincarnated, do they lose their bonus feat and skills?
If the reincarnate spell changes your race, you lose all your original racial traits and gain new ones.
That said, that is simply how the spell interacts with racial traits mechanically. However, some racial traits seem to reflect experience or knowledge rather than genetic/anatomical capability. In such cases, the DM might reasonably house-rule that the character can still access the trait or benefit since only their physiology is changed, not their memories and experiences. There's no official guidance for this sort of thing, so I would simply warn DMs to be careful about allowing this.
Best Answer
Ability scores have a maximum of 20 for player characters.
From the first chapter in the Player's Handbook, section Beyond 1st Level:
But, one might argue, this only applies to ability score increases from leveling up. So what about your case, when someone gains a racial ability that increases their ability score while they are already at 20?
From Chapter 7: Using Ability Scores in the Player's Handbook:
Adventurers, such as a player character, can go as high as 20, but no higher.† To my knowledge, level 20 Barbarians are the sole exception thanks to the Primal Champion trait, which increases their maximum Strength and Constitution (as well as the scores themselves) by 4.
In your case, rules as written, a Half-Orc with a 20 in Charisma who is reincarnated into a Half-Elf would still be at 20 Charisma.
† As always, there are exceptions to the rule. There do exist magical means to increase ability scores above 20; for example, the Tome of Leadership and Influence for Charisma.