Ytdyklly

All the viewpoint characters in my story are orcs and speak Orcish as their native tongue, but some are bilingual: they use English to talk to humans. Additionally, the main character has a magic power: she speaks with djinns telepathically, and it feels to her like she's talking to herself in her head and hearing herself reply. She does this in Orcish often, but can do it in English if she needs a djinn to deliver a message to a human. Her internal dialogue could easily go on for half a page if she needs, say, a djinn to explain a major plot point to her.

So that's 4 different modes of speech: spoken Orcish, spoken English, thought Orcish and thought English. And the narration of the main character's general thoughts and feelings needs to be distinct from the thoughts she shares with djinns.

Making it apparent in context to the reader which is which is not a problem. I can just say so. However I thought it might be handy to have a typographical convention so once the pattern is established I don't have to spell it out every time.

My first thought was that non-italic text could indicate Orcish and italic text could indicate English. Blocks of right-justified text with no speech marks and no narration could indicate the main character's internal telepathic voice, while all the narration and ordinary speech would be left justified and laid out in the traditional way.

However, I'm concerned that having right-justified blocks might be ugly as heck to the reader and/or look bad in a manuscript. Is there a better way?

I agree that the right-justified text blocks are ugly as heck. I'd recommend italics for non-English and a non-quotation punctuation mark for telepathic dialogue. Mostly it's a matter of deciding what standard looks best for you and making sure the reader understands.

As an example, here's what mine looks like:

Normal English dialogue - no italics: "What are you grinning about?"

Telepathic dialogue - angle brackets, italics: <Wait! Don't touch that!>

Internal dialogue - italics: I wonder if that's always been there.

Demonic, elven or other fantasy speech - quotation marks, italics: "Istjak vaharr?" (Not sure whether you're planning to have your Orcish text translated for the reader or not. Another option is to add things like "he replied in Orcish.")

As Rasdashan says, consistency is key.

Some authors use italics to indicate telepathy. Depending on formatting alone could get lost in publication if they don’t understand why you have justified your text.

Consistency is key. If some Orcs are bilingual but no humans are, any Orc speaking to a human would be speaking English. Establish it early on. Perhaps Orcish has sounds that are very difficult to pronounce for humans, so none try. The humans might not see a need to communicate with Orcs.

Karte approached the four humans entering his land. He stopped before
getting too close. Never approach strange humans too close, but they
are all strange. The ungainly language they spoke was one he had been
chosen to learn. He had learned it quickly. “Why are you
here?”

“You speak our language.”

“Yes. Why have you come?” Karte needed to know. Perhaps another could
answer. It would be tiring, but he had few options. Why are these
humans here? Is the truce broken?

“We are going across, but have become lost.”

They seek the healer who lives in your lands. They need his help with an illness plaguing them. It would please me if you let them pass.

Karte nodded. These little humans had bigger problems than they knew.
He would observe them, see that they did not stray. “Keep to the path
you are on. Do not turn from
it.”

“Where does it lead?”

Karte did not answer, but turned and moved away.

Given that you are writing in English, and the majority of the time your Orcs are speaking to each other in Orcish (but translated to English for the reader), then the best plan I believe is to treat both spoken Orcish and English the same, like normal dialog, and only convey, if needed, that one or the other is being spoken as relevant to the story (since it is assumed in most cases it will be Orcish translated to the reader).

On a rare occasion when you might give an actual Orcish term, there is still no need to do anything special, as the reader will pick up on it simply by not knowing what the word(s) is(are), but some hint of explanation should accompany it (or a footed/endnoted translation if it is vital): "Gradzit! Ferbog nor taak," she greeted the newcomer in friendship.

For internal, self-dialog, the most common convention in fantasy literature is the italicizing of direct thoughts (like one speaking to oneself, or one speaking in their mind "to" someone else without that actually being known what they are saying). George R. R. Martin does this regularly in his Song of Ice and Fire series (first book is A Game of Thrones), but he was by know means the first, as that convention has been around a while.

However, italics have been used for telepathic speech (when they are not used for self-dialog). An example of that is Juliet Marillier's, The Sevenwaters Triology (first book is Daughter of the Forest).

Assuming you want to use italics for self-dialog, then one solution for telepathic speech was Joel Rosenberg's use of asterisks to offset the mental speech of the dragon Ellergon in his The Guardians of the Flame series (first book The Sleeping Dragon, who is Ellergon). I don't have a copy of the series to verify it, but if some of the quote from this site is correct, then a sample is this:

"Ellegon!"

*Yes, I'm Ellegon. And you are Karl Cullinane.* A paw slapped against stone. *And this is a floor...*

"Enough. I take it you're the company."

*Very clever. I am also transportation. We will camp on the edge of the forest tonight. Just in case you're interested, I've spent a good part of the past year ferrying some of your possessions here, things you left at the base of Bremon. Including one red mare that emptied her bowels all the way across the Waste. I don't think she likes me. But she does look tasty.*

"We are not eating my horse. And are you certain you can carry all of us?"

*No. Actually, I just want to see how high I can get before we crash. Any other stupid questions?*

Now in that series, I believe the telepathic communication was one way (Ellergon spoke mentally, but could not read others minds, and so the characters had to verbally communicate to him, which he could understand). But the point is that you can replace the quotation marks for verbal speech with something, such as an asterisk, to carry on mental conversations. You could, if you wanted to keep all mental activity indicated by italics (which is more easily noticed), then any italicized dialog in asterisks (or whatever) is telepathic communication between entities, and any not is self-dialog.

Hmm. I wasn't so sure that was a good idea. *Do you really mean that?*

*Yes, I really mean it* Do you think I'm an idiot, why would I not mean it.

But it may be more clear keep italics for self dialog:

Hmm. I wasn't so sure that was a good idea. *Do you really mean that?*

*Yes, I really mean it!* Do you think I'm an idiot, why would I not mean it.

Many publishers set their own standards for justification and the choice may not be up to you. On top of that many books are simply justified. As time passes on your work may end up on different platforms and mediums under different publications and for that reason I would be loath to use right justification as a significant identifier. Furthermore, right justification is far from the norm and will stand out, possibly to a degree that you don't intend. Definitely to a degree that goes well beyond simple quotes and italics. As a visual example I offer this for you to see for yourself:

You probably don't want to add anything that is that visually off-putting for your readers. It is potentially distracting and immersion breaking.

+1 Rasdashan for a suggested approach, I have nothing to add to that.