"I wear an orange skirt."
As it's written, I believe the の is indeed necessary. Here's how I understand it: オレンジ色 essentially means "the color of oranges (the fruit)". So on its own, it's a noun phrase, just like "the color orange" would be in English. The の particle in Japanese isn't always possessive; it can function as an adjective-izer, in much the same way "-y" can make nouns into adjectives in English.
For example, "flower (n.)" + "-y" + "skirt (n.)" = "flowery (adj.) skirt (n.)". 花 (n.) + の (p.) + スカート (n.) = 花の (adj.) スカート。"A flowery skirt." (I used "flowery" to illustrate because it works in both languages where "orange" would not.)
So オレンジイ色のスカート sort of means "an orange-color-y skirt" or an orange skirt, in normal English. (I realize now that one might say "an orange-y skirt" in English, but only when referring to a skirt that's kind of orange but not quite.)
I hope that helps.
There are two versions: 1. Orange skirt. 2. Orange-iro no skirt. (Orange-coloured skirt).
The other two combinations are wrong: orange no skirt doesn't need the no, because orange is already an adjective. And Orange-iro skirt without the "no" would mean "orange colour skirt".
Slightly off-topic, but what I still don't get is "yellow". Apparently (according to jisho.org), 黄 (き) means yellow by itself, and it's a な-adjective and a noun; 黄色 (きいろ) also means yellow, and it can also be either a な-adjective or a noun; and 黄色い means yellow too, but it's an い-adjective. Why?? It all feels so redundant.
But more importantly, it makes me wonder whether this could be written as オレンジ色いスカート instead of オレンジ色のスカート. And if not, what's so special about yellow?
it does, yes! the の here indicates that the word AFTER it is a noun, and the word BEFORE it is describing the noun. what you wrote would translate to something like "skirt-y orange color," not "orange skirt." you're making "skirt" describe "orange" rather than the other way around.