Why don't we need pas before plus?
There are different types of negation, you can only have one at a time.
"ne … pas", "ne … plus", "ne … jamais", etc.
Shouldn't it be 'des vêtements'
No, because of the negation.
Il a des vêtements, Il n'a plus de vêtements.
Is this the rule about this? Is the "de" always singular because of the negation?
"de" isn't singular or plural. But yes, you use "de" and no article after a negation.
I just remember that it is always "plus de" almost one word, mentally, even thought it looks like it is separate words.
Whats wrong with aucun?
That would be "he doesn't have any clothes" which is not the same. This is kind of a weird sentence. I assume it means that he's put all his clothes in the wardrobe and it's still not full, but he doesn't have any more to put in.
Why is it son armoire when armoire is femmine?
"armoire" starts with a vowel sound, so you use "son" even though it's a feminine noun. This applies to "mon" and "ton" as well.
"ma petite amie"
Can I use ne...aucun? Il n'a aucun vetement et il veux remplir son armoire.
That's a different sentence. That says that he doesn't have any clothes. The given sentence means that he has some clothes, but not enough to fill the wardrobe.