Dtyjlui

I've already read this post but just wanted to get clarification;

I am new to D&D and have created a Half-Orc War Cleric who was once a soldier...
His back story involves demons and I decided to add Abyssal to his languages, but with disadvantage if needed.

Can I get away with this - without swapping out Keth Grey-Tusk's proficiencies?

I am pretty sure this will be a duplicate, or at the very least, up to my DM. But I wanted to clarify before the start of the campaign.

Up to your GM

Assuming you have free picks of language left, the Player's Handbook tells you to choose any languages you can pick yourself from the Standard Languages --- Common, Dwarvish, Elvish, Giant, Gnomish, Goblin, Halfling or Orc --- or to pick one that's common in the campaign you're playing. However, it also says the following:

With your DM's permission, you can instead choose a language from the Exotic Languages table or a secret language, such as thieves' cant or the tongue of druids.

Therefore, all you need to do is convince your GM to accept the choice of language. The choice of languages is usually not very important in a game, so typically requests like this are easy to accommodate, but of course your GM's game might play up their importance, in which case they're the best person to determine whether the choice of language is bad for the game or not.

If you have no free picks of language left, prepare to argue harder, as you're essentially asking for a free (if slight) bonus to your character's abilities. It might help to point out that Abyssal is, in practice, of relatively little use as the bulk of its speakers are demons who prefer destruction over discussion.

Languages generally come from your race or background.

Half-orcs do not know Abyssal, so this would essentially be a custom background and, as the link you provided points out, such a background may well provide Abyssal as an option.

So ultimately it would be up to the DM. You may want to look at the existing backgrounds first though. The "Soldier" background may be an obvious choice but Acolyte could also apply and that does provide two languages of your choice. There is no reason why you can't choose a background that fits the mechanical benefits you are after and simply provide a different story to go with it.

NB: As Erik pointed out in the comments to your question, you either know a language or you don't by D&D rules. Again, if you wanted to limit yourself as a purely role-playing choice then you could discuss with your DM how this could play out (e.g. an Intelligence check perhaps to understand the gist of a conversation).

From the 5E SRD:

Customizing a Background

You might want to tweak some of the features of a background so it better fits your character or the campaign setting. To customize a background, you can replace one feature with any other one, choose any two skills, and choose a total of two tool proficiencies or languages from the sample backgrounds.

It is possible

The Curse of Strahd adventure includes an additional character background option: Haunted One (Appendix A, pg. 209).

Aside from skill proficiencies, starting equipment, background feature, and suggested characteristics, it includes:

Languages: Choose one exotic language (Abyssal, Celestial, Deep Speech, Draconic, Infernal, Primordial, Sylvan, or Undercommon)

This background choice does require collaboration with your DM if used outside that adventure, as it isn't from the WoTC core books.