The phonology of every language changes over time. Latin is no exception. In the case of consonantal u (or v), it began to shift towards a v sound no later than the 1st century CE, as evidenced by inscriptions that sometimes replace it with b, which could represent a labial [b] or fricative, either bilabial [β] as in Spanish or labiodental [v] as in other Romance languages. In the 2nd century we get direct testimony that it was pronounced cum adspiratione. But these changes are gradual and not universal: there's still some evidence of it representing [w] in the 5th century, when one source makes fun of people for pronouncing ueni/veni almost with three syllables.

For more details about the development of Latin phonology within antiquity, there is no better resource than Sidney Allen's book Vox Latina, 2nd edition 1975.

You can see shifts like this in any language where there are records from different periods. In English you may have heard of the Great Vowel Shift that took place in the late Mediaeval-early Modern period.

In conjunction with all that, it's the continuous tradition of Latin in western European countries that has led to it being pronounced very differently from, say, Sallust's Latin. Different pronunciation shifts happened in each country where it continued to be used, albeit only in academic or ecclesiastical circles. Listen to, say, Mozart's Requiem performed by a German choir and an English choir and you'll see what I mean: the German pronunciation of Latin will be full of ts sounds where English will have ch. And the modern languages often leak into the Latin pronunciation too: an English choir tends to have muddier vowels and crisper consonants than a French choir (especially noticeable in words where you have two adjacent vowels like deus, or in diphthongs like ae).

You might have more luck asking this in /r/linguistics.

Through my limited knowledge of High-school Latin. I know that many of the letters we use today were not in existence in Roman times. Certain letters would take up multiple sounds before they got broken up into new ones.

As time went on English gained more letters and certain letters changed in pronunciation/use.

Latin had no "j," one good example of this is the Latin word "ianator." This is where the English word "janitor" comes from. It is impossible to understand exactly how Latin was pronounced but we are able to get a good guess.

The "i" sound changes based on position of the "i" in the word (in Latin). If the letter "i" comes at the beginning of a word, it is consider a "consonant" in terms of Latin scansion (scansion is figuring out how certain lines in poems were pronounced). This leads us to believe that ianator is not pronounced "e-awn-a-toar" but something along the lines of "yaa-naa-toar." Later on the letter "j" was used to help distinguish the difference between the separate pronunciations of "i."

While I am not positive of the reason that v's made the w sound, I can give a bit of information on it. Latin had no "w" in their alphabet, while English only acquired it's "w" later. If memory serves me right the word water was originally spelled "uuater" and that the double u's in the word made a "double-u (w)" sound. I am not entirely sure of how v's turned into w's, but I know for a fact that all v's in Latin are pronounced in a "w" fashion.

I apologize for lack of sources, I will try to find some if requested when I come home as I am on my mobile.