I can only speak of my own religious experience to describe what oneness means.
When I was an immature strong theist I had what I now regard as crazy ideas on various things and I sought God’s help to teach me what is right and wrong on all matters to do with humanity. Each issue that I considered, as I changed my mind about them, I adjusted myself to the new knowledge. I became anti-war, more sympathetic to gay rights, more sympathetic to the rights of women wishing to have abortions for whatever reason, pro euthanasia, environmentalism, etc., because that is what I knew that God was advising me was the right thing to be done. It was being at one with individual truths, for God was the ultimate truth for me: His laws had to be right. He was God after all.
There then followed a period when the Personal God vanished from my life and I could not find any sign of it. I came under the influence of people who were strongly atheistic and started distrusting my earlier discoveries, treating them as having been a delusional mind games that I had suffered from. I swung like a pendulum to becoming a strong atheist now. There was no God in sight for me. I became more supportive of wars like in Iraq and Libya as an atheist. But I was still exploring truth and examined the technical details of the Big Bang theory and the origins of the universe as well as Evolution and Abiogenesis in great detail. These did not satisfy me that there was no God as Creator. So I swung back to a form of deism and then what I described as atheotheism (one who had not seen any evidence of God, but did not entirely rule out that there may be a God). I explored under this hat for about a year and then had sufficient proof for me as outlined in this thread that there was a God and that he operated Nature through the truth-seeking and oneness mode (by whatever means he accomplishes that I can only hazard a guess).
At each stage of my changes from one form of outlook to another I practiced what I became. That was being at one with truth. This oneness turned into the acceptance of all things as they appeared and was perceived. I became tolerant of Reality with all its warts, like ‘evil’. Oneness with truth became what more than just learning and practising the new things that I found it beame a frame of mind that was advaita, or non-duality. The mind was focussed on the acceptance of Reality. If America stayed in Afghanistan, that was all right, if it came out, that too was allright. Whatever happened was fine by me. I became non interfering in everything, just seeking the best for myself in my very personal existence surrounding my job, my family, my colleagues and fellow posters in internet forums with a live and let live attitude, and accepting the outcome, not as God’s wish but as the matter of fact that it was: Reality. I was at one with Reality. This was through the process of pursuing truth relentlessly, changing my mind innumerable times but when the dust settled I had found Oneness with Reality.
So I coined and developed the word satya-advaita (the practice of oneness with truth) in light of this experience. I have never come into contact with any New Age or religious group so all my knowlege has been part of the process of self-enlightenment. Oneness seemed the most natural word that came to me from what I was actually doing. So oneness means a lot to me. At the end of the search I am at ‘Aham Brahmasmi’: I am in fact the truth, the Reality, the Brahman that Hindus have talked about for centuries; and without having any longer to bring God directly into consideration for I see that He has done his job on me and got me to a destination – of oneness from where I have not budged. That is the truth.
I do not justify anything supernatural except for an atma/soul – I reject karmic rebirths, heaven, hell, etc. I am different to a Buddhist in that I believe in a indwelling spirit that Hindus have called atma which connects us with the truth mechanism of Nature.
I have been mystical all through the past 15 years in search of truth. I studied and still study everything and express it as a review on myself whenever the opportunity presents itself. I have no ulterior motives but to be at one with truth. It is part of the process of what I hope is oneness. It is in the process of moment to moment existence in perfection of thought and action.