Both those with the Ordered Chaos feat, and creatures with alignment subtypes contradicting their personal alignment, are going to have to be very careful with the wording of each aligned effect that targets them. Specifically, some effects ask what alignment they are, while other effects ask what alignment they are not. If you have Ordered Chaos or the chaotic subtype, chaotic is always going to be an alignment you have, and never be an alignment you lack. That fact will guide you through most effects.
Now, the benefit of the Ordered Chaos is worded “beneficially,” in that the examples given are all beneficial, but nothing in the actual rules of the feat actually says that the effect is strictly beneficial. Also, note that word of chaos explicitly says it only includes non-chaotic creatures in its area, which someone with Ordered Chaos “is” (counts as), so the fact that the creature is (counts as) also lawful or neutral doesn’t matter—they weren’t targeted in the first place.
Order’s wrath is similar to word of chaos in this regard: it specifically targets nonlawful creatures. If you are personally LN but have the Ordered Chaos feat, then you are a lawful creature—which means you are not a “nonlawful creature.” As such, order’s wrath does not include you in its effect, and any questions about what it might do to you are moot.
Weirdly, of the core cycle of 4th-level aligned attack spells,1 only order’s wrath actually has this property. Chaos hammer is another example in the Ordered Chaos feat, and is more awkward. Its area entry makes no mention of alignment, so it definitely affects anyone within no matter what. Instead of that targeting entry, it uses the following wording:
Only lawful and neutral (not chaotic) creatures are harmed by the spell.
This relies on “lawful and neutral creatures” being disjoint with “chaotic creatures,” which is not true with Ordered Chaos in play. An LN creature with Ordered Chaos is (counts as) a lawful creature, but also is (counts as) a chaotic creature. The wording is simply ambiguous—but by including it in the list, Fiendish Codex I seems to imply that the intended meaning of the sentence is
Only lawful and neutral creatures that are not chaotic are harmed by the spell.
This is certainly a plausible understanding of the sentence, and usefully it resolves the problems with Ordered Chaos in a manner consistent with order’s wrath—a lawful creature with Ordered Chaos is immune to both spells.
Now, stepping beyond Ordered Chaos, say we have Falls-from-Grace, the famously-LN succubus from Planescape: Torment.2 Her personal alignment is lawful, but she still has the chaotic subtype (and evil subtype) since she is still a succubus. Suppose she is targeted by order’s wrath—does it do anything to her? Well, it only targets nonlawful creatures—she doesn’t fit that description. She is a lawful creature. Order’s wrath does nothing to her. What about if she’s included in chaos hammer, does that do anything to her? Again, the wording is ambiguous on this point—it only makes sense if being both lawful and chaotic is impossible, which it clearly isn’t. Fiendish Codex I implies one interpretation of that line that resolves this problem—in which case Falls-from-Grace is immune to the spell—but Fiendish Codex I’s description of the Ordered Chaos feat doesn’t really have the authority to do that. An errata for chaos hammer (and the rest of the cycle) should have been issued to fix it, but that never happened.
So you can choose to believe the Fiendish Codex I implication, and make Falls-from-Grace immune to chaos hammer. This would make it consistent with order’s wrath, which is good. On the other hand, you can easily read the “(not chaotic)” parenthetical as applying only to the word “neutral”—in fact, this is the more natural reading and the one I expect the authors intended. Then chaos hammer affects a lawful creature like Falls-from-Grace, regardless of whether or not she is also chaotic. This contradicts Fiendish Codex I, so you’ll have to decide if Ordered Chaos has a specific exception for chaos hammer, and whether that should be extended to other spells, or if the mention of chaos hammer was a mistake, and should be ignored. The latter is probably superior, because then Ordered Chaos and having a chaotic subtype work out the same, which is more consistent with Ordered Chaos’s description.
But in both cases, being “beneficial” isn’t the deciding factor—the wording of the effect is. If you find something harmful that only affects the lawful, or only affects the chaotic, those will affect Falls-from-Grace. If you find something beneficial that only affects the nonlawful, or the nonchaotic, those will fail for Falls-from-Grace.
In no situation should you apply the lesser effects for being neutral along with the effects of being a particular alignment at once. Even if someone is TN with the Ordered Chaos feat, order’s wrath should affect them as a chaotic creature, not affect them once as a chaotic creature and again as a neutral creature. This is actually harder to justify, RAW, but nonetheless I consider it pretty clear that this would be inappropriate—as you note, it makes an anti-chaos spell affect a neutral creature more strongly than it affects an actually-chaotic one. That isn’t correct.
Chaos hammer, holy smite, order’s wrath, and unholy blight are rather similar to one another, and are the 4th-level spell found on the Chaos, Good, Law, and Evil domains, respectively.
Note that Planescape: Torment is based on the AD&D 2e ruleset, and in any event isn’t strictly canon. Still, useful to put a name and a face to the character we’re discussing—Falls-from-Grace certainly could exist in 3.5e.