The problem with the sentence is that it's phrasing something in a nonessential parenthetical form—but the inclusion of that information in the sentence contradicts the essential information in the rest of the sentence.
In normal constructions of this type, we can remove the optional information between a pair of commas without it affecting the meaning of the main sentence:
- Amory Blaine inherited from his mother every trait that made him worthwhile.
This is perfectly clear. Every trait that made him worthwhile, he inherited from his mother.
The sentence could also be constructed differently:
- With the exception of a few inexpressible traits, Amory Blaine inherited from his mother every trait that made him worthwhile.
Here, it's saying that almost every trait that made him worthwhile he inherited from his mother. However, a few traits that made him worthwhile were not actually inherited from his mother.
Here's where the actual sentence become problematic:
Amory Blaine inherited from his mother every trait, except the stray inexpressible few, that made him worth while.
If we simply remove that optional information, we end up with first interpretation. But if we include it, then the sentence actually seems to express the second interpretation (meaning it's not really optional after all).
So, which is it?
We don't actually know. There is a contradiction between the sentence's construction and its meaning. In other words, it's ambiguous.
Is the information provided in the nonessential construction actually nonessential—or is it essential information that should have been presented differently?
Compare this unwise construction with something slightly different:
Amory Blaine inherited from his mother every trait, including the stray inexpressible few, that made him worthwhile.
This version is quite understandable. The meaning is that of my first interpretation. He inherited everything from his mother. Some of the things he inherited were also inexpressible. This is how nonessential information should be presented.
Having said all of that, I can't tell you what the sentence means, only that it means one of two possible things. (Further context might resolve the ambiguity.)