‘The New Testament itself is written in a language Jesus never spoke.’

So claims Richard Rohr (The Divine Dance: The Trinity and your transformation) in a throwaway comment.  It is one of a large number of careless and inaccurate statements by this writer.

The two main languages spoken by Jews at the time were Aramaic (in everyday communication) and Hebrew (in more formal religious matters).  But what about Greek?  This language had been spoken in Palestine for several centuries.  In Jesus’ time, its use would have been quite prevalent in the cities of the Decapolis and those, such as Capernaum, that lay on major trade routes.  Additionally, Jewish diaspora returning to Jerusalem and Judea would have spoken Greek.

It is likely, then, that Jesus knew some Greek, but it is not possible to say how fluent he was in that language.  The strongest clue is found in his exchange with Pilate (Mark 15:2–5; Matt 27:11-14; Luke 23:2-5; John 18:29-38).  Pilate would not have been able to speak Hebrew, and is unlikely to have been proficient in Aramaic.  His first language would have been Latin.  But those around him – the chief priests, the elders, and the crowd – would not have understood Latin.  So he and Jesus probably communicated in Greek.

F.F. Bruce (Answers to Questions, p175) says that Jesus would definitely have read the OT Scriptures in the original Hebrew in the synagogue at Nazareth (Lk 4:16-19), and would have used Aramaic in everyday conversation.  As for Greek, Bruce agrees that our Lord would have addressed people such as the Syrophoenician woman and Pontius Pilate in that language.

See this article, and also this article, in which Professor Stanley E. Porter defends his view that Jesus taught in Greek as well as Aramaic.