Despite the long list about to follow, this was a very good showcase and should be quick to get finished. The first two issues are the major ones, everything else are small fixes.

Quest flow
1) If Barzark is killed before you take the quest, Ocrulun will still complain about the smell if you meet him, and if you accept the quest there will be no way to tell him about the warlock already being dead. Now, the problem there is that, logically, the quest would just not happen if you kill Barzark, you'd just find a very confused Altmer with a dead bonewalker in Hlan Oek. And that would be one way to solve it - if a player has killed Barzark first for some reason, there just isn't a quest, and Ocrulun only gives some flavour dialogue. Another way would be to just be cheeky and only enable Barzark after you've accepted the quest. I think both would be acceptable ways to fix this.

2) You need to make sure that you can only get the reward once. Because you have relevant entries both in his greeting and in the quest topic, if you kill Barzark then Ocrulun will first reward you if you mention the quest topic to him, and then reward you again when you speak to him as he is walking toward the river. This is because the journal entries set for returning to Ocrulun after killing Barzog are 50 and 60 respectively, whereas the Greeting 5 reward line plays for any value under 70 (and he also talks about you keeping the ring in it, even though you might not have even brought the ring). I would suggest just not using Greeting 5 to play the reward line, and let it always go through the "curse of foul smell"-topic. That way you also don't need to worry about it not triggering because the bonewalker gave you a disease just now.

3) The line where Barzark tells you that you shouldn't have put on the ring because Ocrulun won't be able to handle the bonewalker alone is very unlikely to ever play. It filters to Ocrulun being dead, but the game doesn't consider him dead until you actually return to Hlan Oek and it gets to process his death. And after you get the journal entry for killing the bonewalker, Barzark gets a different line. That means this one line can only play if someone puts on the ring, goes to Hlan Oek, doesn't deal with the bonewalker, and then goes back to Barzark. This doesn't break anything, so it's not really a bug, I just thought I should point this out since you might not have been aware about what it would take for that line to trigger. If you want Barzark to react to you having put on the ring at all, you need to make the ring script set a local on him and filter to that.

Objects
4) Ocrulun needs to have Corpses Persist ticked. Otherwise, once he is dead his body is subject to the game's corpse despawn mechanic, and if it's gone you get a journal entry about him dying despite there being no corpse to be found. This could conceivably happen if the player travels to Hlan Oek after putting on the ring, and then spends a while in the city doing something else.

5) The bonewalker doesn't have a SoundGen set - that's not your fault, neither does the vanilla bonewalker you copied it from, but it IS something our validator complains about. So you should set it to Bonewalker_Greater.

6) Ocrulun doesn't wear any armour, but his unarmoured skill is only 5. Generally, NPCs should be set up to utilise their equipment or lack thereof, even if it won't matter in most cases.

7) The poison damage enchantment on the ring is pretty powerful, better than the enchantments used on Dire Viper weapons, and at range too. I'd tone it down a little.

8) Barzark's ID should be m3, not m7. Even though he is involved in a quest in map 7, the ID should still follow his actual position. This is even more important for the script (see below)

Scripts
9) The script on Barzark sets his map number to 7 instead of 3. Almas Thirr is in m3, and so that's where the map variable should put him.

10) The Khajiit check on Bazark doesn't follow the usual format for checks like that. Best practice is to put it at the very bottom as

if ( T_Local_Khajiit )
    return
endif

set T_Local_Khajiit to 1
set TR_Map to 3

Conversely, if a script is assigned to an NPC that isn't a Khajiit anyway (in your case Ocrulun), all references to the Khajiit check should be removed (there is no need to set it to -1), and the final part of the script should instead be

if ( TR_Map )
    return
endif

set TR_Map to 7

Note that both of these are designed so that they only get the locals assigned once, because the next time the script hits the "return" first and ignores the bottom part.

Dialogue
11) I guess Ocrulun is technically outside the northern city walls, but saying he is north of the striderport would be better directions for the player. Especially because there aren't actually walls where the striderport is.

12) If you use %PCRace in dialogue it usually requires having an alternate line for if the speaker and the player are the same race. This is especially true for elves. Ocrulun calling you "High Elf" when he is also one AND would use the term "Altmer" anyway is incongruous.

13) I suggest putting a Goodbye at the end of all the lines in curse of foul stench (and Greeting 5 if you want to keep the lines there) that set Ocrulun to begin the "having a bath" sequence. Forced Goodbyes like that are a good indicator to the player that whatever happens next happens outside the dialogue window.

14) "mumble under his nose" - maybe I've just never heard that particular version of the idiom before, but I think this should be "breath", not "nose".

15) You have "this mer" in the latest rumor topic and "this Khajiit" in the curse of foul smell topic. It should be "that", as it's talking about people not present.

16) I'd suggest putting the ShowMap "Almas Thirr" command in the line where Ocrulun tells you that he met him in Almas Thirr, right where you also get quest stage 10. That way it's only done once, instead of having a tiny lag every time you click on Almas Thirr. You should also add something like "in Almas Thirr, north of here", or "down the river", something that at least vaguely includes directions to justify why it makes a map marker appear.

17) "Septims" should be lower case.

18) You have a double his in the "%Name has commanded his his bonewalker to follow"-lines

Additional notes (not part of the showcase process)

• This isn't an error and so you don't need to fix it, but: try to not introduce new locals if you don't have to. By using "bathtime" and "bathday" for Ocrulun, you've now forever added them to the long list of locals that will show up for picking dialogue filters. Unless you're dealing with very complex scripts where the name of the local is necessary for documentation, try to use locals that already exist in other places, mainly control and its many derivatives (controlQ, controlQ1, controlV etc.). Keep in mind that a local is just an arbitrary string of text that gets assigned a value - DoOnce doesn't inherently have anything to do with something happening once, it's just convention to use that name for a local like that. And as long as that string is unique to this particular object (an NPC in this case), it doesn't matter what it's called and where else it's been used, unless it's one that's used to mark large groups of NPCs (like the TR_Map locals).
• It's fine because this was for the showcase, but usually .esps should always start with TR_mX (or other prefix as applicable) so they're easier to find. Ideally they also shouldn't have spaces or apostrophes in them, as that makes them bothersome to use in command lines like for the validator.
• Barzark always refers to the player in third person (he/she, %PCClass etc.) - this is actually not how Khajiit in Morrowind talk most of the time, despite the memes. They do say "you", it's only themselves they always refer to in the third person. It's not totally absent either (e.g. J'Saddha does, Ajira sometimes does), so it's not an error per se for Barzark to talk like that and you don't need to change it unless you want to. But just keep in mind for the future that not every Khajiit you write should do it.
• Hlan Oek is already very heavy on misc quests, it might be worth retrofitting this quest to one of the towns in the Coronati Basin. But we can talk about that on discord after the showcase is done.