Through him (δι' αυτου). Christ.

We both (ο αμφοτερο). "We the both" (Jew and Gentile).

Our access (την προσαγωγην). The approach, the introduction as in Romans 5:2.

In one Spirit (εν εν πνευματ). The Holy Spirit.

Unto the Father (προς τον πατερα). So the Trinity as in Ephesians 1:13. The Three Persons all share in the work of redemption.