From BibleStrength

Not Identicality

See also Trinity

Oneness refers to a sharing of spirit, because a spirit can inhabit multiple bodies (e.g. the Holy Spirit). It does not mean different individuals are the same, which should be evident from John 17:11,20-22; since Jesus says Christians are one with God the Father and Him in the same way He and God the Father are with each other. Christians are no more identical to God the Father and Jesus than they are to one another. God the Father, Jesus the Son of God, and the Holy Spirit are all individuals, but God the Father is greater in power, authority, and knowledge. (John 14:28; Mark 13:32; 1 Corinthians 15:28)

A Sharing of Spirit

This is how oneness works: God pours out His spirit on "all flesh" as foretold, so that they are all one with each other. That is how Christians become one body of Christ, through having the spirits of God the Father, the Holy Spirit, and Jesus inside of them. By having the same spirit all Christians are made to spiritually be seated in heavenly places together and share a spiritual bond of fellowship. (Eph. 2:5-6)

Holy Spirit is an Person

The Holy Spirit is an individual not a force. The Bible says the Holy Spirit can be grieved and is our access to God the Father.

Now, Jesus, God the Father, and God the Holy Spirit all are said to bear witness in Heaven.

However, there does seem to be a progression in authority. Jesus is above all but God the Father, since Jesus helped create all that exists. Jesus is above humans and every other name. God the Father is the only one above Jesus.

Oneness even applies to marriage as well it seems:

It is interesting that the book of Acts as well as other books repeatedly speaks of the Christian church worshipping God with a oneness or singleness of heart, mind, and spirit. (Acts 1:14, 2:1, 2:46, 4:24, 4:32, 5:12,15:25, Romans 12:16, 15:5-7, 1 Corinthians 3:8, 2 Corinthians 13:11, Philippians 1:27, 2:2, 1 Peter 3:8)

Paul uses the analogy of the Christian body to describe how Christians are one as a church, with different members but one whole. (Romans 12:4-8, 1 Corinthians 10:17, 12:4-31, Colossians 3:15)

There's a lot of confusion over what the Bible means when it speaks of oneness, hopefully this helps clarify somewhat.