America is a nation of immigrants, and we borrow words from every language and culture. In addition, we also are constantly inventing words. New words come from technology, advertising and the media. After all, we have "app" and "bromance" now. New words will always be invented.
Many words in the English language can be traced back to Greek or Latin, or the classical age. When the Normans conquered Britain, the French language exerted its influence on English, particularly on those that wanted to sound powerful. We can see this when we discuss food, for example beef is drawn from the French word for beouf (I hope that's spelled correctly) rather than from "cow." Perhaps the most recent influence on English has come from technological innovation rather than other languages.
Italian has influenced English in the field of music, entering primarily through opera. Words like crescendo (gradually become louder) and allegro (rapid tempo) are Italian loanwords and used in their borrowed Italian forms. Latin has influenced law and sciences, including medicine. For example, jurisprudence (philosophy of law) is derived from the Latin words jūris prūdentia meaning "knowledge of the law." An example in medicine is trachea that entered Middle English from Middle Latin trāchēa, which itself is derived from the earlier Latin word trāchīa that was borrowed into Latin from the original Greek loanword trācheîa. Government, which is closely akin to law, is also influenced by Latin. An example is the Constitutional right of habeas corpus derived from the Latin words habēre (to have) and corpus (body). Short, simple words, like house and come, are original Old English words that made their way up through Middle English to the present day.
The language that has influenced English most in terms of government and law would have to be French. French is the immediate origin, at least, of words such as governor, legislature, and judge.
As far as medicine goes, Latin is one language that has had a great impact. Words like renal, adrenal, and abdominal all come from Latin.