God is the Father is unique, omnipotent, uncreated, eternal, invisible, only true, creator of heaven and earth and everything within—seen and unseen. He accomplished the creation through the Son and the Spirit. He is the father of Jesus Christ.
The Holy Spirit is the spirit of God, through whom everything was created. He preached the way of salvation (τας οικονομιας). In the fullness of time he was poured out upon mankind in order to create them anew for God. He is the mediator of the knowledge of the truth, indeed, he is truth itself.
I should add that in this interesting interview with N.T. Wright, Wright makes a similar statement about the nature of the Gospel as a reference to a reality that is the case (Jesus is Lord) and not the process of salvation (justification by faith). To quote: "The problem with us Evangelicals is that we use the word "Gospel" to denote the system of how someone gets saved. I really want to emphasise this: we are not justified by believing in Justification by Faith, we are justified by believing in Jesus." Great point! Wright's presentation of the content of the gospel, however, is very Pauline, whereas I think Irenaeus has the entirety of Scripture in view. Perhaps that is the advantage of reading Paul in his canonical, and not just historical context. On this, see Childs' latest book.