Unlike David, I do think that there are things that we can say that UUs generally believe (tho always taking into account the right of conscience and that there will be some UUs who disagree). Actually, I don't think that David and I disagree on this; it's just a matter of what we choose to emphasize. For example, in general, UUs believe in "ongoing revelation." That is, we believe that the truth is constantly being rediscovered by each new generation, by each new person. In general, UUs do not believe that the truth is handed down and then "set in stone". Related to this, UUs tend to believe in the inherent goodness in humans. Because we have this inherent goodness in us, we have the ability to recognize truth when we see it, and the ability to take on the responsibility of our own spiritual development. This isn't to say that we never make mistakes; obviously we do; but in the grand scheme of things, we will choose good.
These are cornerstones of our faith tradition. Of course, they are not unique to us. I know people from many different religions who share these beliefs and I feel great kinship with them. But I do think that UU is unique in how strongly we emphasize freedom of conscience and the ongoing search for truth and meaning. It is for this reason that it is difficult to say what UUs believe, because we're always cognizant that someone else's conscience may not agree with ours and that the search is not over - what we believe now may change. To be a UU is to be comfortable with uncertainty. (Or at least to able to tolerate uncertainty. I can't say that I'm always comfortable with it.)
As for the unity of God. Yes, traditionally the Unitarian side of our heritage was so named because they rejected the trinity. However, that meaning has since been expanded to include the unity of all faith traditions. Among our ranks, there are Christian UUs (both trinitarian and non-trinitarian), Hindu UUs, Pagan UUs, Muslim UUs, atheist UUs, Buddhist UUs. We get along because ultimately we believe that these are all different expressions towards a unifying truth. A truth that is measured by how well we treat each other and not by the ideas that we espouse.
Here is how I look at it, and here I am speaking just for myself and not other UUs. I believe that God is good. And because of that I believe that God cares more about what is done in God's name than whether we got the details of God's metaphysical status correct. Even tho I personally view God as unity, I do not argue with people who view God as trinity or any other number. To me, that's like arguing over whether's God's eyes are blue or brown. It has no bearing on what's really important. And that is, as a believer, how do you express your faith? Does it make you more compassionate towards others, more passionate about justice, and more happy in your own life? Or does it make you meaner or apathetic or more irritable or more hurtful? Given that God is good, I can't help but believe that this is the basis upon which we will be judged. If I remember correctly, Islam holds this view as well. In the end, when we face final judgement, all of the actions of our lives will be presented to us one by one and our own souls will judge whether or not we measured up. There will be no doctrines to hide behind, only our own consciences and whether we truly believe that the good we did outweighed the bad.