Re: So I'm descended from an ancient turkey?
No, only the language.
People don't seem to realise that the British Isles weren't so much "invaded" by the Celts, Romans, Angles, Saxons and Normans as "taken over" by them. What were considered major battles at the time often consisted of just a single percentage of the land's actual population. What happened was that a band of thugs came over, beat up the resident thugs, and took over the reins of power, imposing their own cultural preferences on their subjects.
The Ancient Britons spoke a language very similar, but not identical, to Welsh for the most part, although there would have been some very strong variations in accent and dialect even back then due to the lack of good communications. (Think of the difference between Geordie, Scouse, Brummie, etc. today. And those exist despite the invention of mechanised travel and both radio and TV.) Similarly, when the Romans "invaded" and usurped the land from the Ancient Britons, the Celtic cultures slowly faded away in favour of the Roman one.
That does not mean millions of Italians came to England and kicked all the locals into Wales. Instead, the cultural changes spread organically throughout the land—in part, because running water, underfloor heating, sewage and other infrastructure, and very lucrative trade, were a major step up from the cold, muddy, Celtic stockaded villages full of hovels they replaced.
The locals simply compared what they had with the new options made available to them and decided to trade up.
The Welsh and Scottish Highlands proved a major obstacle to the Romans and so saw very little Roman influence, which is how the Celtic culture remained in that neck of the woods. The Romans didn't bother invading Ireland at all. The Romans never entirely conquered the south-west of England either.
Modern Welsh is not the same language as old Welsh. It includes some influences from the later invaders of England, including a number of adapted loan words, but it does retains the Celtic base-20 counting system that didn't disappear entirely from the English language until well into the 18th Century. ("Four score and seven years ago...") Modern French still retains that component, hence their bizarre counting system. ("Quattre-vingt-dix" for "90". In Belgium and Canada, they just say "novante". In Italian, it's "novanta".)
When the Romans left, the power vacuum led to the rise of Angle and Saxon influence from what is now northern Germany. The feudal system meant that all the commoners saw was a change of ownership at the local manor or castle. Naturally, the newcomers imposed their own cultural values on the natives.
And then came the French Vikings in 1066. Old French is the source of most of English's Latin influences. Old English was basically a dialect of Frisian up to that point. Italian itself didn't really enter the picture until the Renaissance era, but that only really affected some arts and crafts rather than embedding itself right into the heart of the language. It was a brief Victorian fad for all things Latin that changed "fall" into "autumn". Italy didn't even exist as a single country back then.
(Incidentally, the common military term for a "war game" right up until WW1 was "kriegspiel". The British Royal Family is German and there was a very strong pro-German culture up to that time as a result. The Saxe-Coburg and Gotha family changed its name to "Windsor" in 1917 due to the anti-German propaganda of the time.)
"Sabato"—literally "Sabbath"—is the Italian word for Saturday today. But "Saturday" itself derives from "Saturn's Day" and came from the Normans. (Italians use "Domenica" instead of "Sunday", which is another word derived from the country's most famous religion: It translates approximately to "Day of Our Lord" and shares the same root as "Domini".)
The above shows just how far Christianity influenced the Italian language. (The Papal States had a lot to do with it.) But that religion clearly didn't impose similar changes beyond the Italian peninsula. Instead, early Christian missionaries preferred to adapt to the existing customs, so the old Norse weekday names remained.
And that's just one tiny aspect of how languages change over time. It's a very, very complex subject.