First, some background. (Also, note this is rather speculative as all else...)
I'm not going to argue against the notion of a soul "doing work" in the physics sense. Naturalists, as you know, who are adherents of a religion whose fundamental tenant is "there is no God", would insist that human consciousness is strictly a function of biochemistry, thus rendering your question irrelevant.
Personally, however, I don't buy these claims, and it seems that science doesn't, either; at least, there is as yet (TTBOMK) no fully satisfactory explanation of human consciousness which relies strictly on naturalist causes. (There's a whole other topic of conversation here I would love to go into, but we're just a wee bit off topic.)
We do, however, know that the brain is largely responsible for the control of the body. That is, it seems highly unlikely that souls, however they interface with this material world, do so by, say, directly exerting a force on your arm. Rather, they work via the brain somehow to cause nerve signals to be sent to your muscles. Thus, the minimum force/power necessary is only that which is responsible for your brain sending the appropriate signals. Given what we know about the effects of brain damage, "muscle memory" and the like, it may even be that what the soul communicates is highly abstract (thus, requiring little "bandwidth") and that the biological brain is largely responsible for determining how to act on such high level imperatives. I mention this because it would suggest a much lower value for whatever quantity is being measured.
To put it differently, the soul is perhaps like an operator sending a robot the instruction "pick up that object". Because this is information, it can be conveyed with very little energy. The brain is like the computer that parses that instruction and decides how to carry it out, sending more detailed instructions to the body. The body, then, contains powerful motors (muscles) and fuel reserves which enable it to perform the task.
Various sources place the brain's power (in the physics/energy sense) at between ten and twenty watts. This may be an upper limit.
A lower limit is hard to quantify, since we don't know the mechanism by which souls interact with the brain. I suspect, however, it might be very, very low, possibly on the order of manipulating handfuls of electrons.
You also asked:
Does the Bible, or any other Christian scripture ever have an event where a minimum power output or force of a human soul? [sic]
As noted in a comment, I'm not sure what, exactly, you're asking here, but my guess is "no". "Scripture", according to mainstream Christians, would essentially consist of "the Bible", which was written over a span of time not later than roughly 2,000 years ago. Back then, there was no such thing as "molecular biology" and at best a very limited understanding of electricity. Thus, no basis by which to explain such operations as detailed above. Also, lest someone insist that God would know such things even if the audience at the time did not, keep in mind that the goal of Scripture is to instruct us on theology, not science. Yes, there is science in the Bible (and solid science, despite claims of Naturalists to the contrary), but such almost always occurs when serving a theological purpose. As I can find no theological purpose to the question, it is highly unlikely that God would supply such information "on a silver platter" as it were.
Even extending the definition of "Christian scripture" to include self-proclaimed Christians (i.e. JWs, LDS), we run into much the same issues; the documents, though coming into existence much more recently, still predate the knowledge necessary, and said knowledge is anyway not an objective.
So, unless God Himself suddenly starts publishing to scientific journals, it's unlikely you'll find any "scriptural" answers.
But wait! You also asked:
Has Any Christian sect calculated it or explained it?
It may be clear from the first section that this ought to at least be possible. To the best of my knowledge, the answer here, then, is "not yet". Neurophysiology is one of the frontiers of science, and as you may have gathered, there remains debate whether human consciousness (sapience) is fully explainable in purely naturalistic terms. I'm not aware of any Christian scientists actively working in this area, but it also would not surprise me if we eventually do learn that there necessarily exists something beyond the cells of the brain. Should such a determination be made, an investigation into the nature of that mechanism is almost sure to follow, and one of the consequences of such an investigation might well be an understanding of its mechanism of operation, and perhaps an ability to quantify the power/energy requirements thereof.