How do Trinitarians respond to this contradiction of dogmatic 'oneness'?

Trinitarian understanding is very Biblical and must be Separated from Tritheism, Oneness theology, Unipersonal God and other forms.

The Father- From who all things consist

The Word - in Time named Jesus - Proceeding forth from the Father, externally in and with the Father.

The Spirit - Proceeding from the Father and the Word.

This must be differentiated from the Oneness Position which is : the unitarian or unipersonal deity named Jesus has two natures: divine, the mode of the Father/Holy Spirit and human, as the mode of the Son of God (though not God the Son).

We just need to prove the pre-existence of the Word/son. By Scriptures, and then that the Pre existent Son is Jesus in Time.

Now to your question, Oneness - Essence It dosen't make it two Gods

This Being of God is Expressed in Person, not Modes, and in scriptures we see this in a Person called the Father, another Person called the son, and another called the Holy Spirit.

Joh 10:30 I and the Father are one.”

The word translated “one” is not in the masculine, but in the neuter gender. It expresses union, but not the precise nature of the union.

So we allow context to define the union The nearest context makes that Union of Purpose, design and Plan.

A more broader context allows for the position of early fathers, which is as referring to the oneness or unity of nature between the Father and the Son

Their reasons will be, *The question was about Power and his being the messiah not Plan and Purpose, (verse 24)

• The Jews Understood him as to declaring equality with God. (Verses 33)
• Jesus also did not deny that it was what he meant, he only Corrected their understanding of the Application of the word god to men. Yet set himself distinct from all Men.
• The Jews understood him in this manner.

And AUGUSTINE was right in saying the "We are" condemns the Sabellians (who denied the distinction of Persons in the Godhead), while the "one" (as explained) condemns the Arians (who denied the unity of their essence).

So why did Jesus literally say at John 10:30, "I and My Father We are one?" John 10:27-29, Jesus says the following. "My sheep hear My voice, and I know them, and they follow Me; vs28, and I give eternal life to them, and they shall never perish; and no one shall snatch them out of My hand. vs29, "My Father who has given them to Me, is greater than all; and no one is able to snatch them out of the Father's hand."

Jesus is clearly saying that the sheep are equally safe in His hand and in His Father's hand. The power of the Son is equal to that of the Father, and while this is the contextual point of reference, much more is implied.

Jesus asserted the essential unity of the Father and the Son in the word "one" (hen). It is a neuter number to indicate equality of essence, attributes, design, will, and work.

Jesus distinguishes the "I" from the "Father" and uses the plural verb "are" denoting "we are." Thus these words separate the persons within the Godhead, but "one" asserts their unity of essence or nature as identical.

The Jews understood what Jesus was claiming because at John 10:24 they ask, "How long will You keep us in suspense? If You are the Christ, tell us plainly." Jesus does not say "I am Christ," but "I and my Father, We are one"--God!

At John 10:31, "The Jews answered Him, "For a good work we do not stone You, but for blasphemy; and because You, being a man, make Yourself out God."

At this point Jesus brings up Psalm 82:6 and the subject of "Gods," why? (John 10:34-38.) Jesus is taking the Jew's statement about Him blaspheming to its logical conclusion to show that they are being inconsistent.

In effect, Jesus is saying, "If you say that I am blaspheming, you must also hold that God is blaspheming because He said to those by whom the word of God came, "ye are gods."

It is not "blasphemy" to claim to be the Messiah. There is no scholarship which supports this interpretation. Furthermore, MANY people before and after Jesus claimed to be the Messiah and were never charged with, let alone convicted of "blasphemy." It is, however, "blasphemy" to claim to be THE Son of God.

How do I know? All one has to do is read the trial record at Matthew 26:57-67. At vs63 the high priest Caiaphas ask Jesus to swear as to His identity. "And the high priest said to Him, "I adjure You by the living God, that You tell us whether You are (1) the Christ, (2) the Son of God." Whether is defined as "expressing a doubt or choice between alternatives."

At Luke 22:70 Jesus states, "Yes, I am." Now back to Matthew 26:65, "Then the high priest tore his robes, saying. "He has blasphemed! What further need do we have for witnesses? Behold, you have now heard the blasphemy:vs66, "what do you think?" They answered and said, "He is deserving of death!"

The FACT that Jesus was convicted of blasphemy for saying yes is proof that He was claiming deity. The act of claiming deity for one's self IS blasphemy,, unless you really ARE God. The Jews simply did not believe Jesus, just like many do today.

It was that very statement "I and my Father are one." that provoked the Jews to take up stones. What is it that the Jews understood Jesus to be saying with this statement?

I and my Father are one. Then the Jews took up stones again to stone him. Jesus answered them, Many good works have I shewed you from my Father; for which of those works do ye stone me? The Jews answered him, saying, For a good work we stone thee not; but for blasphemy; and because that thou, being a man, makest thyself God. - John 10:30-33

A similar exchange at John 5 provokes a similarly extreme response:

But Jesus answered them, My Father worketh hitherto, and I work. Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God. - John 5:17-18

Apparently Jesus referring to God as his Father (and I believe that literally he said "the Father of me") was understood by the Jews in a way that is very favorable to a trinitarian theology: Not that Jesus is the Father but that being the son of the Father (who is God) affords him an equality with God.

If Jesus' claim to be the son of God were akin to the usage common to the Jews of his day there would have been no violent reaction. Some contend that the Jews misunderstood what Jesus was saying but it is not reported to us in that fashion and is, therefore, conjecture.  In fact, John 5:18 records not the Jews words but the Apostle's record of what the Jews understood and it is significant that he does not tell us that they misunderstood.