In answer to your question, I wouldn't recommend taking the pairings to be six factors that add up to the human so much as multiple ways of expressing the same thing that is the human.
infinite eternal freedom psychical
finite temporal necessity physical
All of the terms on the top represent wide possibilities. All of the terms on the bottom represent limitations. In other words, as infinite beings, we seem to have no limit. As eternal beings, we will live forever, as free beings we can do what we want. As psychical beings, we can think as we will (think Descartes' Meditation IV argument about will and intellect).
For him "physical" does mean having a body, but "psychical" is not at all meant as a reference to brain.
The point is that we are a synthesis of the two sides in each case. We are both limited and unlimited, and the challenge of being human is to be a self that relates itself to a self and in the process relates itself to another that is the base of its power. In other words, we have a task of using our capacities to understand ourselves.
When we are out of whack -- with either the infinite or finite pole of any relation dominating, we fall into error. If we are obsessed with our necessity, we cease to act. When we are obsessed with our possibility, we dream absurdly, because our dreams have no anchor. When we are overly concerned with the temporal, we are in unknowing despair. When we are overly concerned with the eternal, we are in knowing despair. When we are too obsessed with the physical, we neglect our minds. When we are too concerned with our minds, we forget that we are embodied.
There's quite a few good texts on understanding the Sickness unto Death. For instance, the first two or three articles in the International Kierkegaard Commentary: Sickness unto Death are summaries of how the argument works. I've published on it as well this year in International Philosophical Quarterly. There's also a volume of essays by C. Stephen Evans from 2004 (not quite sure on the date).
