I've known of researchers chipping off varnish to analyze the chemical compounds, others who swear it's the types and seasoning of the wood that creates the sound. The most exciting thing about the research being done with the CT scanner is they can analyze the exact thickness of the wood at all parts, measure the volume of air inside the body, and take measurements they were never able to do without either guesswork or taking apart the instrument (which nobody wants to do with a Strad, because once you put it back together you've likely ruined its superior sound forever!).
I played a Strad once. I was a freshman in high school. The Baroque Violin Shop had one at the OMEA convention. I played Malaguena or some other silly thing. I probably sounded awful. But even my playing at that age was instantly elevated by this thing. I don't want to attribute any mythical properties to any one instrument, but people often wonder how it is that a violin can sell for hundreds of thousands of dollars while one can buy many other professional level instruments for a tenth of the cost. Instrument value is determined by the reputation of its maker, its age and condition, and its sound, though this last count is incredibly subjective. I've played $3000 dollar instruments I've liked better than $30,000 instruments.
The other issue is that the violin has to fit your technique. If you're a kid taking lessons, the $30,000 violin's response could be so quick it's a little disorienting because you haven't developed the muscular reflexes to work with that (I've experienced that many times. As I improve, I'm able to sound exponentially better on a more expensive instrument). It's also a matter of developing a relationship with your instrument. After you've been playing one for a time, your muscle memory becomes acquainted with where the harmonics lie. There's a personal fit that has to occur. Some people like a wide neck on the violin; mine is comparatively thin. I like the facility I have with shifting as a result.
It's like living together. You know all the faults of your instrument, but you are in this permanent (or at least long-term) arrangement. For example, the instrument I used to have had an incredibly brilliant sound on the e string. It was clear and sweet, and when I go back to it today I'm shocked at how good it sounds up there with just a little vibrato. But the g string was terrible. Past third position, it was so cloudy and uneven that there was no coaxing a good sound out of it. My current instrument is more balanced overall, but less brilliant in the upper register. It has a wolf on the high C on the G string. And it resonates well in the extremities but I have to work harder to get the same sound on the middle strings.
The thing that makes violins and other stringed instruments so fragile is their material. Wood expands and contracts due to changes in temperature and humidity, and not only that, the wood is thin to allow for interior vibration. A well-made instrument must not buckle under changes; though improper care from the owner can lead to open seams and cracks.
Of course, no matter how well-made the violin, there are so many other factors that can influence one's sound: the brand of strings you use, placement of the interior sound post, the interior volume of the instrument where the sound resonates, amount of bow hair in contact with the string, too taut or too loose of a bow, the material of the bow (carbon fiber vs. pernambuco wood), how much rosin is on your bow (which has an effect on the amount of friction generated between the horsehair and the string), even the style of shoulder rest (I've heard that this can have a slight impact on the vibration of the body due to the way they clip to the sides of the instrument). Not to mention all the technique they teach you to in order to achieve a particular sound!
Interesting side note: Pernambuco is toxic, and many bow makers die young (40s and 50s) from lifetime exposure to the wood shavings. I learned that on a tour of a bow making school. I have a carbon fiber bow. I prefer it because it does not warp in humid weather. I like its consistency and lightness, though my bow in particular is rather finicky for spiccato and tremolo strokes. It has to be just so, in about an inch of bow. I don't have a lot of room to maneuver.
And if you were wondering, I do listen to Stratovarius, the band. I posted on here once about my love of the song Stratofortress. First of all, that is one of the most hilariously metal song titles ever. Secondly, it uses harpsichord (or at least, a synthesized harpsichord).