I will leave my first answer as it is.@Mark Edward has said in his comment, regarding my response to the question,"This response consists of identifying what the list refers to. It does not answer the chief question being asked: Why does the order of the list vary"?
So why does the order of the list vary? The answer is quite simple.
The list varies to enable the reader to pay more attention to the wording.
5:9c For you were slain, and by your blood you ransomed people for God
from every tribe and language and people and nation
7:9a After this I looked, and behold, a great multitude that no one
could number, from every nation, from all tribes and peoples and
languages, standing before the throne and before the Lamb
10:11 And I was told, "You must again prophesy about many peoples and
nations and languages and kings."
11:9 For three and a half days some from the peoples and tribes and
languages and nations will gaze at their dead bodies and refuse to let
them be placed in a tomb
13:7 Also it was allowed to make war on the saints and to conquer
them. And authority was given it over every tribe and people and
language and nation.
14:6 Then I saw another angel flying directly overhead, with an
eternal gospel to proclaim to those who dwell on earth, to every
nation and tribe and language and people
17:15 And the angel said to me, "The waters that you saw, where the
prostitute is seated, are peoples and multitudes and nations and
languages."
The scriptures that appear to be causing you confusion are,
10:11 And I was told, "You must again prophesy about many peoples and nations and languages and kings."
17:15 And the angel said to me, "The waters that you saw, where the prostitute is seated, are peoples and multitudes and nations and languages."
In your question you observe,
Twice (in 10:11 and 17:15) he replaces out tribes (with kings and
multitudes respectively). But even in the other five places, he
switches up the ordering every time.
I think the intent of the author is to bring into our focus 7:9, and the word "multitude".
7:9a After this I looked, and behold, a great multitude that no one
could number, from every nation, from all tribes and peoples and
languages, standing before the throne and before the Lamb.
In this scripture it can be observed that "all tribes" are included in the great multitude.Before this selection was made, all tribes must have been selected from, (not a multitude of tribes),but multitudes of tribes that inhabit the earth.Hence the wording "all tribes." For understanding read here. "Multitude or Multitudes." Note the wording when Jesus ministered to all the different people.
The point that i am making is,the author does not substitute the word "tribes" with the word multitudes because tribes are already included in the multitudes,The author challenges the reader to use his own intuition.In short, tribes = multitudes in 17:15.
The next scripture in question is 10:11,
10:11 And I was told, "You must again prophesy about many peoples and
nations and languages and kings."
The emphasis in this scripture is on the word "kings," but unlike 17:15 where the word multitudes is added in second place,kings is added at the end.This draws the readers attention to the wording before kings.Please now look at my list which contains the seven scriptures and the bold in 10:11 and 17:15.
In 10:11 in the list, the sequence, peoples and nations and languages is used.Also in 17:15 we can pick up this sequence again (or nearly,if not for the word "multitudes.")
peoples and multitudes and nations and languages."
There is no other place in the list where this sequence of, people,nations and languages, is so apparent other than 10:11 and 17:15.But why does the author substitute tribes for kings in 10:11? I think the reason for this is to keep the readers focus on the wording,peoples and nations and languages and also to direct the reader to the King of Babylon.
Daniel 4:1 Nebuchadnezzar the king, unto all people, nations, and
languages, that dwell in all the earth; Peace be multiplied unto you.
Now view the list from the book of Daniel here
With reference to the list in the book of Revelation you say,
Seven times in Revelation, John describes people in a fourfold
manner,Undoubtedly the sevenfold reference is intentional given John's
penchant for sevens. But it's also interesting that he never repeats
the exact sequence or description across the seven instances.
I will answer you by saying "that in the book of Daniel,the author describes people in a threefold manner in a sixfold reference,and it's also interesting that he repeats the exact sequence across the six instances.
Conclusion
So why does the order of the list vary? The answer is quite simple.
The list varies to enable the reader to pay more attention to the wording.