How did English words like vocal, vision, and victory come to be pronounced with a modern v unlike wine, wall, and worm?
"Worm" has /w/ because it isn't from Latin
Worm is not from Latin at all. It's a native English word cognate to Latin vermis; each language inherited its own form of the word from the common ancestor of English and Latin (Proto-Indo-European), which is supposed to have had a word *wr̥mis with [w] and a syllabic "r". This is different from borrowing because it means worm was subject to all of the sound changes between Proto-Indo-European and English, but none of the sound changes between Proto-Indo-European and Latin. The /w/ > /v/ law is a Latin change, not an English change, so it never applied to "worm".
Native English words don't start with /v/
In fact, English does not natively have word-initial /v/ at all (well, there are a handful of words with initial /v/ from Germanic /f/ due to dialect mixing, like vixen and vat, but they are not regular inherited words).
In Old English, the sound [v] only existed word-medially between voiced sounds; it is thought to have been in what is called "complementary distribution" with the voiceless equivalent [f]. This means that for any given environment, only one of these sounds was possible. The standard phonological analysis of this fact treats Old English [v] as a predictable variant of a single "phoneme" /f/. (Diachronically, old English /f/ generally developed from either proto-Germanic /f/ or proto-Germanic /b/).
In Middle English, the law of complementary distribution for [f] and [v] was lost, leading to the establishment of a new phoneme /v/. It is thought that an important factor in this was influence from Romance languages such as French which had developed word-initial /v/. English has a lot of loans from French that start with /v/, such as "very". (There were also some native developments that helped establish the phonemic distinction between /f/ and /v/, such as the loss of word-final schwa.)
Loans from Latin with /v/ are either from French, or are modern loans
Loans from Latin with the /v/ sound like vocal, vision, and victory either came through French (or other related Romance languages), or are even more recent modern learned loans (made after English had an established /v/ phoneme and a tradition of using it for "v" in Latin words).
Loans from Latin with /w/ are old loans into Germanic
Wine and wall are old loans taken into the ancestor of English when it still didn't have a /v/ sound. (In fact, the borrowing of "wine" seems to predate the split of the extant Germanic languages, and that of "wall" also apparently predates at least some splits between Germanic languages.) At this time, /w/ was evidently felt to be the closest equivalent to the Latin consonant (which might also have been closer to /w/ at this time period, perhaps something like [β]).