Jesus spoke Aramaic.
That's the truth. Everyone knows it. There can be no doubt about it. Mel Gibson even made a movie about Jesus where everyone spoke Aramaic and nothing else.
Except, that's not true.
I'll offer two pieces of evidence to prove my point.
First, at the beginning of the Christian era Palestine had been a Hellenistic colony for about 200 years. About 40% of the population were Greek. They spoke Greek, wrote Greek, and thought Greek. Even government records were issued and kept in Greek.
If Jesus spoke to these people, He spoke Greek.
Imagine a situation similar to modern day San Diego. Most of the population is Hispanic, but the official and most commonly spoken language there is English. So the Hispanic population speak enough English to get by. And there is a common polyglot spoken that people call "Spanglish".
So we can conclude that the same kind of thing happened in Palestine in Jesus' day.
He probably spoke Aramaic as the language of His choice. And He probably was educated in Hebrew as the language of His religion. And then He probably spoke Greek and some combination language Greek-amaic joining Greek and Aramaic.
My second argument is similar.
When Jesus asked Peter, "Simon, do you love me?", He unquestionably spoke in Greek. It is obvious that this is so, because the conversation makes no more sense in Aramaic than it does in English. But in Greek, it begins with the sense of "Do you worship me?" and ends with "Do you like me?"
Therefore, Jesus spoke Greek as part of His normal, everyday conversation.