Tolkien's major characters are more complex than that. There is no one "domain of power" for Melkor. Throughout the stories in The Silmarillion, Melkor brings destruction and uses his power in different ways. And like almost every major villain in literature, he has exceptional cunning.

But you won't find the simplification you're looking for in Tolkien's writings, which is why you didn't find it here.

Well the question is some what interesting. according to ainulindale and valaquenta , all the valar of the middle earth have a certain power or powers. like manwe and winds , ulmo and fresh waters and so on . but they also have other descriptions that are somewhat faded by the choice of the writer . for example about tulkast is said that he is fast in friendship and anger and "not a good advisor" meaning tulkast is a hard and strong fellow kinda god yet he dosent have enough wit and wisdom. but when it comes to melkor it specificly said that he has a little of all the other valar have . that to me means that he has control over wind for example but not as much as manwe has grip on it . or he has the power of craft yet he is not as full in it as aule . but the other thing that j.r.r tolkien was so focused on was the wrath and ruin that melkor would set where ever he would walk. for example the most privet part of the lives of the valar was before the coming of elves and in that time every single one of the main valars had made something and had tolerated labour. but the only deed that melkor had done in that time was the ruin he had brought to other of the valars and their doings. so in my opinion melkor was a shameless lier and had power in ruining valuble things .:)

Didn’t it say in the Ainulindale that he had multiple “domains of power” and had power from multiple sources.

Even though he was mightiest of the Valar, Melkor went against Eru’s song of creation and therefore wasn’t given dominion over an aspect of reality unlike his brother Manwe and air, or Tulkas and strength.

Actually if you read the early Silmarillion carefully, Melkor shared similar interests to Aulë and Melkor's desire to have his own creations apart from Eru was one of the factors that put a wedge between him and the rest of the Valar. It seems like Melkor's inability to "give life" just made him more bitter.

@Fandylic you have a point as while Aule created the dwarves out of impatience for the arrival of the children of Eru and repented when Eru accosted him (with Eru adopted the Dwarves) Morgoth desired to control all of creation or at least twist and corrupt everything what Eru and the Valar created into designs of his own mind including Eru’s children as Morgoth saw himself as equal to Eru early on as he desired “the flame imperishable” which belonged to Eru alone.

In my opinion, he probably didn't have one.

In the Ainulindalë, Ilúvatar's big quote is all about how nothing can happen that does not begin with him. Hence, if Melkor became evil, he was meant to be evil. Nothing is ever said about Ilúvatar's power being overthrown. The Valar are fallible, but Ilúvatar is not.

That being said, I have heard an interesting theory about Melkor being sort of like Varda, but for the humans. Sort of being their most honored god, and their source of guidance.

If the theory about Melkor being like Varda for humans is correct, no wonder the world is so messed up.