I have always been taught that "Oneness" groups believe that God is manifested in three Personalities sometimes called ways. I also have been taught that these groups are cults.
There are other groups out there that believe as you said. They don't believe in the Trinity. They believe the Holy Spirit is another name for God or believe that the Holy Spirit is the power of God. I don't think these beliefs qualify to be called "Oneness".
I copied this from the web.archive website. It is an org. Sorry I cannot link with my user name. This should help give you ideas to use when debating these people.
"Jesus is our Lord and Saviour. What He says is the truth. What He commands, we do. If we refuse to acknowledge this we cannot claim to be Christians.
Christ's last instructions to His disciples were explicit: "Full authority has been given to me in heaven and on earth; go and make disciples of all nations, baptize them in the name of the Father and the Son and the Holy Spirit, and teach them to obey all the commands I have laid on you. And all the time I will be with you, to the very end of the world" (Matt.28:18-20, Moffatt).
This commandment given by our Lord leaves no possibility for modification -- it is an instruction to make disciples of all and baptise them in the Name of the Triune God. All nations have not been baptised -- the unbelievers are in the majority. Missionaries have not been to the "very end of the world" -- some parts remain unevangelised. Therefore we are to do as Jesus says, baptising in the name of Father, Son and Holy Spirit until the end. There is therefore no provision for baptism in the Name of Jesus alone even though all authority has been given Him, because all authority belongs to the Father and the Holy Spirit as well.
United Pentecostalists (if I understand them right) teach that Jesus (Yahshua/Yeshua) is Father, Son, and Holy Spirit. If so, then He was talking to Himself at Calvary and praying to Himself throughout His ministry. Jesus Christ was not two persons, as the Gnostics taught, but one. He taught His disciples to be one with the Father in the same way that He was one with Him (John 17:22). When speaking of the Father He always referred to both of them as "we". If the United Pentecostalists are right, then we are Christ too, and that is New Age doctrine!
United Pentecostalism is a dangerous heresy that robs God the Father of His glory. It misapplies a selection of scriptures that speak of Jesus's divine Fatherhood without considering all the rest. Even the term "godhead" (Ac.17: 29; Rom.1:20; Col.2:9, KJV) is meaningless in a United Pentecostalist (UP) setting because the word implies that there is more than one Person who is God -- otherwise how could there be a "head"? There is no Godhead in UP doctrine.
Consider another problem. If Jesus is the Father and also the Son, how come "Jesus the Father" knows when Jesus the Son is returning to earth but not Jesus the Son?? "No-one knows about that day [the second coming], not even the angels in heaven, nor the Son, but only the Father" (Mt.24:36, NIV). The UPC doctrine is nonsense in this light. Why not simply accept that the Father and Son are two Persons but one God, as the Bible teaches?
Actually, to be frank, I am not sure you are asking the right question. I am not saying that you have not been called to be a "Pentecostal" but I am wondering what all your reasons are for framing such a question, whether you are becoming a Pentecostal because of family tradition {the enquirer's brother is a Pentecostal minister -- ed. note} or because you are absolutely sure this is where the Lord wants you to be. I think you have other questions that you must ask Him. Of one thing I am sure, though, it is that UPC on the Godhead doctrine is false and therefore dangerous -- it is contrary to the Apostolic Doctrine of the New Testament (Rom.16:17) and should therefore be shunned."