Verses 17-18: And came and preached peace to you which were afar off, and to them that were nigh. For through him we both have access by one Spirit unto the Father. Jesus came to preach the message of peace to those which were afar off (Gentile), and to them that were nigh (Jew). Now they both have access to the Father, unlike before when only the Jews had access.
Verse 19: Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God; He is still building off of what he had said in 2:11-12. In other words, now that the enmity has been removed and the Gentiles are no longer strangers and foreigners, they are now fellowcitizens with the saints, and of the household of God. Contextually, this is clearly saying that Jew and Gentile have been made one in the Body of Christ. Why would he say that? - Because it wasn't true before that (Mat_15:21-28). Also, it is not saying that the church has now been made a part of Israel. Nope. Never.
Incidentally, that is not what Romans 11 was saying either. The Body of Christ is not in view in that chapter but Gentiledom as a whole.
Built Upon the Foundation
Verses 20-22: And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone; In whom all the building fitly framed together groweth unto an holy temple in the Lord: In whom ye also are builded together for an habitation of God through the Spirit. These verses can only mean one or two things. 1. The church was built upon the foundation that was laid by the Old Testament prophets and the teachings of the Twelve, or... 2. The church was built upon the foundation of some other prophets and apostles. Ephesians 3:4-5 says clearly that the Old Testament prophets and apostles did not know what Paul knew regarding the mystery, so it can not be talking about them.
Who were these prophets and apostles? It would seem they are the ones who is going to speak of in Ephesians 4:11-13. If that is the case, these were grace apostles and prophets, who according to the text were appointed until we all come to the unity of faith. I am of the mind at the moment that these offices were discontinued after the completion of the Paulene epistles. That being the case, these were also the ones that he was referring to in 1 Corinthians 12:28 as well.