Some of the books of the old testament were originally written in Aramaic.
Actually I believe only parts of Daniel, Ezra, and Jeremiah have Aramaic. You may be thinking of the Targum which are Aramaic translations of the Hebrew.
With the new testament it amazes me how so many of Jesus's apostles were so fluent in Koine Greek
Are you implying the gospels were originally written in Hebrew? I have heard that theory. Although I don't think it holds water for most books, there are a few early 'church fathers' who wrote that Matthew penned his book in Hebrew. May be something to that.