The phrase spiritual oneness, in obscure at best, without more specifics to the question the answers will be unsatisfying. Having said that there a few variations worth considering. Spiritual oneness is not expressed in the Biblical accounts, there is the "Jesus Only" movement, also known as Oneness Pentecostalism or oneness theology, it teaches that there is only one God, but denies the tri-unity of God. In other words, oneness theology does not recognize the distinct persons of the Godhead: Father, Son, and Holy Spirit. It has various forms—some see Jesus the Christ as the one God, who sometimes manifests Himself as the Father or the Holy Spirit. The core doctrine of Oneness Pentecostal / Jesus Only is that Jesus is the Father and Jesus is the Spirit. There is one God who reveals Himself in different "modes."
This teaching of the Jesus Only / Oneness Pentecostals has been around for centuries, in one form or another, as modalism. Modalism teaches that God operated in different forms or modes at different times—sometimes as the Father, sometimes as the Son, and sometimes as the Holy Spirit. But passages like Matthew 3:16-17, where two or all three Persons of the Godhead are present, contradict the modalistic view. Modalism was condemned as heretical as early as the second century A.D. The early church strongly contended against the view that God is strictly a singular person who acted in different forms at different times. They argued from Scripture that the tri-unity of God is evident in that more than one Person of the Godhead is often seen simultaneously, and they often interact with one another (examples: Genesis 1:26; 3:22;11:7; Psalm 2:7; 104:30; 110:1; Matthew 28:19; John 14:16). Oneness Pentecostalism / Jesus Only doctrine is unbiblical.
The concept of the trinity of God, on the other hand, is present throughout Scripture. It is not a concept that is easily grasped by the finite mind. And because man likes everything to make sense in his theology, movements such as the Jesus Only movement—not to mention the Jehovah’s Witnesses—regularly arise to try to explain the nature of God. This simply cannot be done without doing violence to the biblical text. Christians have come to accept that God’s nature is not subject to the limitations we might like to put on Him. "For my thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts." Isaiah 55:8-9
If we can’t understand His thoughts and ways, we accept that we cannot fully understand His nature, either.