Paul is the author but Acts 19 might give us from insight about the audiences.
Acts 19:8-10 Paul entered the synagogue and spoke boldly there for three months, arguing persuasively about the kingdom of God. But some of them became obstinate; they refused to believe and publicly maligned the Way. So Paul left them. He took the disciples with him and had discussions daily in the lecture hall of Tyrannus. This went on for two years, so that all the Jews and Greeks who lived in the province of Asia heard the word of the Lord.
1. There was a Jewish synagogue.
2. The Christians was called "the Way."
3. There is a place called "Hall of Tyrannus."
1. Paul argued about "the Kingdom of God." (for three months)
2. Paul has discussions daily. (for two years)
If you think there are chop sections, then it could be previous discussions that the audiences were aware of. There were demonic possessions there Ephesus (11-16), people have practiced sorcery and burning of scrolls (19), there was a silversmith who business declined and caused riots (23-41), a temple of a non-existing goddess Artemis (27 and 35), there was a theater (31), and Revelations 2:1-7 say there was false apostles and the Way hate the practices of the Nicolaitans. What can you draw from this for Ephesians 2?