He believed there is one substance of the Father and of the Son and of the Holy Spirit. The substance or Godhead is eternal, i.e., without beginning and without end. It is immortal, i.e., incapable of dying. It is impassible, i.e., incapable of suffering. It is immutable, i.e., not able to be changed. It is incorporeal, i.e., without a body or physical existence. It is incomposite, i.e., not made up of distinct parts or elements. It is uncircumscribed, i.e., we cannot trace a figure around it. It is omnipresent, i.e., it fills the whole universe. It is invisible, i.e., we cannot see it with our eyes.
As we can see, Theodoret's way of doing theology in his Demonstrations by Syllogisms is mostly apophatic, meaning, he describes God by telling us what God is not, e.g., not physical, not mortal, not visible, etc. What's very noteworthy is that he wrote that the Godhead is "simple and incomposite." We find then in his aforementioned writing what is perhaps an Eastern acknowledgement of the doctrine of divine simplicity, a very Western doctrine.
Regarding the Incarnation, he taught that it happened at conception. The name Christ indicates pure Godhead and pure manhood, and the latter is body and soul. Because the Godhead is immutable, the Incarnation was not a change of the Word into flesh but an assumption of the flesh by the Word. Theodoret likened Jesus' body to a temple for that reason. Regarding the Atonement, he taught that because we sinned we needed, "a sacrifice free from every spot." Therefore Christ kept His body and soul, "clean from the stains of sin [and] for men's bodies gave His body and for their souls His soul." After the Resurrection there still remained, and there always will remain, the union of the two natures in one Person. On account of His flesh the faithful are members of Christ.
For Theodoret, everything he taught was in accordance with the Holy Scriptures and the fathers of the Council of Nicaea. Moreover, to believe and confess the right doctrines about Jesus Christ is to be obedient to Scripture. As a Lutheran I like his standards and high view of Scripture!