the usage of "such that"

Solution 1:

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."