Merriam-Webster's Eleventh Collegiate Dictionary (2003) offers a clearer picture of what "such that" means and how it works than does the dictionary discussion quoted in the posted question. It does so, however, in two parts, considering such first as an adjective and then as an adverb:
such adj (bef. 12c) 1 ... b : having a quality to a degree to be indicated {his excitement was such that he shouted}
...
such adv (bef. 12c) ... 2 : in such a way {related such that each excludes the other}
Although this dictionary doesn't break out "such that" as a distinct phrase, the quoted definitions describe two senses in which "such that" may be used: to mean "of such a kind or of such character or to such a degree that," where such functions (in Merriam-Webster's opinion) as an adjective; and to mean "in such a way that," where such functions (in Merriam-Webster's opinion) as an adverb. In each case, "such that" serves as an abbreviated form of the appropriate longer phrase.
If you aren't sure which longer phrase the writer has in mind in a particular instance, you can replace "such that" with each longer phrase and see which one makes more sense. In the example given in the posted question,
The damage was such that it would cost too much money to repair.
the longer phrase that the author shortened to "such that" appears to be "of such a kind that":
The damage was of such a kind that it [the damage] would cost too much money to repair.
But it would be easy enough to create a similar sentence where "such that" has an adverbial character and means "in such a way that":
The house was damaged such that it [the house] would cost too much money to repair.
The shorter dictionary example quoted in the posted question—
power such that it was effortless
—is a fragment, so it's difficult to identify with certainty the intended longer form of the phrase shortened to "such that." Moreover, some sentences are ambiguous without further context. Consider this complete sentence:
The emperor wielded power such that it was effortless.
where it refers to, say, "crushing the rebellion." We could read "such that" as meaning "in such a way that" (implying that the emperor wielded power ruthlessly) or as meaning "of such character that" (implying that his power was so complete that resistance was easy to break). In this case, readers can't tell which meaning of "such that" the author had in mind, unless there are contextual clues in nearby sentences.
Native English speakers don't worry about whether they are using the word such in "such that" adjectivally or adverbially—and I recommend that you not get caught up in that question either. From the perspective of coherence, the practical issue is whether "such that" stands for "of such a kind or of such character or to such a degree that" or for "in such a way that."
According to the Corpus of Contemporary American English this odd construction doesn't appear to be a mistake. Furthermore, it seems to be most prevalent in the Academic Register:
(search string: [space] such the [space])
That being said, it is quite rare; it may give pause to readers, which is something to consider.
I too am an editor in the scientific realm, and I find that many authors love to use esoteric stuff like this (maybe under the assumption that it adds clout to their opinions somehow). It's hard as an editor to suggest corrections for clarity, especially in this register, so I'd gauge your author's demeanor.
Good luck!
Best Answer
The general difference is and is inclusive and or is exclusive.
With nouns:
When the subject of object is A and B or A or B and A and B are nouns, e.g. “You can have A and/or B”, and indicates “both A as well as B”, whereas or indicates either A or B but not both.
You can have an apple and an orange. – You can take two fruit. You can have an apple or an orange. – You can take one fruit.
With verbs:
When and is used to address verbs, the actions of both verbs may be applied to the object. And also states that both actions are possible.
You can fry eggs and boil them. This is advice for eggs in general - the action of both verbs is possible.
When or is used to address verbs (choices of the action applied to one object), or states that only one of the actions is possible.
“Here is an egg. You can fry it or boil it,” i.e. you can do one of the actions but not both - you cannot fry it and then boil it.
EDIT TO ADD
Such as = for example. What follows is a list that contains examples in apposition to a previously mentioned noun or action. Thus we can simplify your example to
It is triggered by {birthdays and anniversaries}. -> either a birthday or an anniversary will trigger it or both together will trigger it.
It is triggered by {birthdays} or {anniversaries}. -> Either a birthday or an anniversary will trigger it but both together will not.
In this case, the distinction is pedantic and in your case, both are possible and the example is understood as
It is triggered either by birthdays or by anniversaries - it doesn't matter which.
Or
It is triggered by birthdays and it is also triggered by anniversaries.
The problem is with the verb “trigger” – this is a punctual verb. Punctual verbs have no real duration – they are instant. Because they are instant their action cannot affect two things at the same time and therefore the reader imagines the case of a birthday and an anniversary occurring at the same time. or imagines only one example - the case of a birthday or the case of an anniversary.
The difference is clearer when a durative verb is used. Durative verbs contain an implied duration of action in their meaning. “To read” is a durative verb – it takes time to read.
Compare a durative verb
It is read by the girl and the boy.
It is read by the girl or the boy.
(Grammatically, both are correct but express different ideas.)
With a punctual verb
It finished at 8 pm and 9 pm - this is wrong.
It finished at 8 pm or 9 pm - this is correct.