I understand that there's the Gojuon order for あいうえお and so forth, but if I
had list with Katakana アイウエオ, do I order it all like あいうえおアイウエオ, or do I order
it like あアいイうウえエおオ? Consequently if I have Jukugo in this same list, does it
get interspersed with the Hiragana and Katakana? Or does it get separated and
added to the end?

Trying to find a concrete answer but my textbook is providing with no
solutions.
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kanji readings katakana hiragana sorting-order
How do I alphabetize a list with Hiragana, Katakana and Jukugo?
You simply "alphabetize" by sound in **aiueo** order, regardless of how it's
actually written.
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This is a problem that is not and will not be completely solved.

In general, you sort by the reading of a word, in the gojūon order, regardless
of the actual character. If you had a list of nonsense words like [あかさ, アカコ,
赤{あか}け], they would be sorted to an ascending order like this:

>   * 赤{あか}け
>   * アカコ
>   * あかさ
>

This is not part of gojūon, but computers sort characters so that dakuten
(like in ば) and handakuten (like in ぱ) come after は: `sorted([ば、ぱ、は])` →
`[は、ば、ぱ]`. Small kana come before normal-sized kana: `sorted([づ、っ、つ])` →
`[っ、つ、づ]`.

You will have to decide yourself what to do with words that have the same
reading but are in ひらがな, カタカナ or 漢字. One way is to not care and just treat
them equally, but you can also keep the list organized and choose to sort
hiragana before katakana and katakana before kanji. If there are many words
with the same reading but different kanji, you can use the code point of the
kanji as a fallback (more about that later).

However, as @Jimmy said in comments, names (and even some words written in
kanji) can have multiple readings. You will not know how to sort for example
the name 淳子, because it can be read じゅんこ、あつこ、きよこ、あきこ. Also the word 日日 can be
read ひび、ひにち or even にちにち.

Then there are marks that depend on the previous syllable.

  * Long vowel mark 「ー」 should be read as ア in シャワー.
  * Iteration marks (ゝ、ゞ、ヽ、ヾ) indicate repeated kana, possibly voicing it in the process. They are not commonly used and it might not be worth the trouble to convert them to kana for sorting.

Kanji repetition marks (々) might need to be converted to the preceding kanji
if the dictionary used for reading lookup doesn't index words that frequently
use them. Example: 日々 → 日日.

If we're talking about computer-based sorting, the program sorting the words
or names could check word readings from a dictionary, and in uncertain cases
choose the most common alternative. This kind of functionality doesn't exist
by default in any programming languages that I know of, and they sort the
strings according to the code point of each character. [This happens to be
alphabetical in English](https://en.wikipedia.org/wiki/ASCII#Character_set),
but as you can see, if the string is not converted to upper- or lowercase
completely, uppercase will always come before lowercase.

[Here is a corresponding list for
hiragana](https://en.wikipedia.org/wiki/Hiragana#Unicode) and [here for
katakana](https://en.wikipedia.org/wiki/Katakana#Unicode). Because hiragana
starts at `0x3040` and katakana starts at `0x30A0`, hiragana will be sorted
before katakana like UPPERCASE vs. lowercase by default. The code page is
mostly in gojūon order (excluding rare kana like ヴ/ゖ), and one way of sorting
would be to convert every word to katakana or hiragana and sort by that.
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