I think I can give some answers as to how Naminé and Lea are continually able to use the DCs.
But first, DiZ.
We must remember that after his apprentices betrayed him and banished him to the Realm of Darkness, Ansem the Wise grew so hateful and vengeful that he essentially became, for all intents and purposes, a denizen of the darkness, just like Maleficent. You can even see during KH2/CoM/Days that his eyes are colored yellow, a trademark sign of a darkened heart.
Because of this, Ansem gained the abilities to use the Corridors of Darkness and change his form and all that other fun stuff. When his Kingdom Hearts encoder device exploded, it likely did the same thing it did to Riku and basically washed all of the darkness in his heart clean. This resulted in the loss of his dark powers, and also (at least temporarily) of his memories. As to where he got the black coat from, go figure. Ansem did say "anything could happen" when the device exploded; maybe KH just decided to give him some new digs.
Anyway, onto Lea and Naminé.
Something we have to remember about the both of them. Both of them were Nobodies for a period of time. And Nobodies, being creatures born in the region teetering on both light and darkness, could be considered as denizens of both. Therefore, they could have access to the abilities routinely used by both. Roxas, for instance, was able to use the Keyblade, up till now a weapon used exclusively by denizens of the Realm of Light. But each Organization member also had access to the powers of darkness, such as being able to produce Corridors. Same goes with Naminé—even though she was created from a heart of pure light, she still is, by virtue of her being a Nobody, a person who straddles the boundary between being a creature of light and darkness, allowing her access to abilities from both realms.
Now, as to the question of why Lea is able to use certain dark abilities, like opening Corridors, even after his recompletion, is a trickier problem. Lea is obviously not a dark-hearted individual, and since his eyes aren't yellow, we have definitive proof that he lacks the requisite attributes as a human being to possess dark powers.
But...
Then again, so did Riku.
Riku never gained yellow eyes except when he was masquerading as Ansem SoD during KH2. And yet he still had access to the powers of darkness. Why? Well, because he gave himself up to the darkness once before. Apparently, the mere remnant of the darkness to which he allowed himself to be exposed still gave him access to the powers of darkness even though he never completely fell to it.
Ergo, what I surmise is this: I believe that since Lea subsumed his Nobody Axel into his recompleted being, he also inherited Axel's dark abilities that he possessed by virtue of his transformation into a Nobody.
But, then, if that's the case, then why have the other ex-Nobodies never used this ability following THEIR recompletion?
Well, let's consider each case:
1. Kairi—It's true she absorbed Naminé at the end of KH2, and since Naminé could use the CoD, we might assume Kairi could then inherit this ability. But we must remember that she is still a Princess of Heart—probably incapable of utilizing dark powers regardless of her Nobody's influence, since she has a heart of pure light.
2. Sora—While it's also true that Sora absorbed Roxas, a Nobody who could also use the dark corridors, it must also be remembered that, like Naminé, Sora and Roxas are not exactly a one-to-one match like the other Somebody-Nobody pairings are. Roxas, after all, as we all know, is a mixture of both Sora and Ventus, and Sora became recompleted even while Roxas was still alive. This means that, from the point that both regained their being, they each branched off into being truly different people. Axel and most of the other Organization members, however, have always been mere extensions of their Somebodies—retaining their memories, their physical attributes, their personalities—there really is very little to distinguish their Nobodies from their original selves, and so perhaps that allows for the abilities gained in their Nobody forms to carry over more easily into recompletion. Roxas, however, would not so easily be able to transfer such abilities back to Sora, because the two of them are more distinct from each other than the others are from their original persons. That's not super-strong reasoning, but it is something. Following this logic, we may conclude that Sora is simply unable to use the CoD because Roxas was sufficiently unique as a person so as for there to not be a strong enough coherence between him and Sora for his abilities to carry over.
3. The ex-Organization members—Regarding Ienzo, Dilan, and Aeleus, we can follow the previous trains of reasoning and assume that they actually DO have the abilitiy to use the Corridors of Darkness, but simply choose not to. We must recognize that Ienzo, Dilan, and Aeleus appear to be VERY different people than their Nobody counterparts, and none of them seem particularly keen on meddling with dark powers anytime in the future. Ienzo is particularly regretful of his actions, and probably wants so little to do with the darkness at this point that he would sacrifice the convenience of its powers. Even, of course, willingly became a Nobody once more to plant himself in the new Organization, so we saw him regain those dark powers; I'm not certain of any evidence that would suggest that Even, while he was a recompleted person, was unable to use the Dark Corridors before becoming a Nobody again. I don't think there was much time between his recompletion and his re-separation to really know for sure.
So, those are my theories. I know I must have written a book on it by now. If anybody can think of anything I've missed, please feel free to reply.