What level of will-power do humans have according to Luther?

To what extent Luther thought human's have 'free will' is actually not fully disclosed in any of his writings. In general Luther opposed all notions of free-will, as those espousing the term always implied some ability (no matter how insignificant) to perform some good work (even if qualified by a 'cooperation' with the Spirit). Luther firmly believed and taught that no man could do 'anything' good unless regenerate by the Spirit of God through faith apart from any work. So no man had free-will as humanity only had the ability to sin.

The background history to Luther's book, 'The Bondage of the Will', was in response to a criticism of his teaching which Erasmus of Rotterdam had published under the title of De libero arbitrio. Erasmus chose this subject, that is their clear difference in their views about human freedom, as a point of argument to publicly commit himself to a position opposed to Luther. He had been pressured to make his position known and was previously reluctant to take a clear side. Now the gloves were off so to speak, and so Luther criticized Erasmus view of freedom in his book as a response. The fact that the book is a response, rather then a orderly thought out treatise of a subject Luther was proposing, is what leaves some things unclear, where not related to his opposition to Erasmus view.

Having this difficulty of determining Luther's view admitted, we may yet at least scope Luther's view under the envelop his own pen has left us. To simplify things we can skip the whole book and start with the 'conclusions' that he presents at the end.

First, he declares there is no such thing as free-will (as suggested and understood by Erasmus and anyone supporting man's ability to do good prior to his being justified by faith):

For if we believe it to be true that God foreknows and predestines all things, that he can neither be mistaken in his foreknowledge nor hindered in his predestination, and that nothing takes place but as he wills it (as reason itself is forced to admit), then on the testimony of reason itself there cannot be any free choice in man or angel or any creature. (Luther's Works, Vol 33, Page 293).

Earlier in the book Luther explains the concept of foreknowledge as being not just a prediction of what men decide but a deterministic power, being also omnipotent and having care for what happens in his universe. He uses cases such as Pharaoh and Judas to argue that they had limited freedom in that they could not but fulfill God's prophecies concerning their actions.

We know that the Father begets willingly, and that Judas betrayed Christ by an act of will; but we say this willing was certainly and infallibly going to occur in Judas himself if God foreknew it. Or if what I am saying is still not understood, let us have two sorts of necessity, one of force with reference to the work, the other of infallibility with reference to the time; and let anyone who listens to us understand that we are speaking of the latter, not of the former; that is to say, we are not discussing whether Judas became a traitor involuntarily or voluntarily, but whether at a time preordained by God it was bound infallibly to happen that Judas by an act of his will should betray Christ.

But see what Diatribe (Erasmus) says here: “If you look at the infallible foreknowledge of God, and his immutable will, Judas was necessarily going to turn traitor, and yet Judas could change his mind.” Do you really understand what you are saying, my dear Diatribe? Leaving aside the fact that the will can only will evil, as was proved above, how could Judas change his mind so long as the infallible foreknowledge of God remained? Could he change God’s foreknowledge and make it fallible? (Luther's Works, Vol 33, Page 192)

The point is that Luther says if God foreknew that Judas would betray Christ then it only stands to reason that Judas could not alter his destiny no matter what he did. Luther does not say it but the implication is sort of like Spielberg's 'Back to the Future' film. One small event in time might have numerous consequences upon the future, therefore God not only determines the way humanity is unfolded over time, but anything specifically foreknown by God are fixed absolutes that can never be altered. The foreknowledge is deterministic not only spiritually but to some degree materially. For example, Judas could not have killed himself before the appointed time, otherwise the prophecy of God would fail. However Luther does not attempt at all to enter into the complexity of what God's foreknowledge and infinite power imply, he merely asserts that they exisit. Or in other words as already quoted, literally 'that nothing takes place but as he wills it'.

An important point to add, to avoid any misunderstanding is that Luther does not mean Judas had no free choice, rather that his choice to follow his desires were free, but that he had no ability to change his desire. In other words free-choice is basically the ability to freely sin, if there is such a term as free-choice. Judas was not compelled by God to follow after his wicked desire. Only the circumstances surrounding his life were so disposed by God that his desire would be brought about, freely, into the eternal plan of God according to his eternal will.

So, without complicating things more, or changing the subject, let me become more direct in answering the original question. It is not my intention to fully explain Luther's book or his opinion overall about human freedom as that would be very difficult to do without writing another book. Regarding to what degree men do have a kind of free choice there are very few quotations to chose from. Possibly the best two are these that follow.

First, more or less still in his introductory remarks, Luther throws away the term free-will as something only God properly has, but allows some sense of it to be retained if that is what his readers prefer:

But if we are unwilling to let this term go altogether—though that would be the safest and most God-fearing thing to do—let us at least teach men to use it honestly, so that free choice is allowed to man only with respect to what is beneath him and not what is above him. That is to say, a man should know that with regard to his faculties and possessions he has the right to use, to do, or to leave undone, according to his own free choice, though even this is controlled by the free choice of God alone, who acts in whatever way he pleases. On the other hand in relation to God, or in matters pertaining to salvation or damnation, a man has no free choice, but is a captive, subject and slave either of the will of God or the will of Satan. (Luther's Works, Vol 33, Page 70)

His distinction about 'beneath him' and 'above him' can more or less be translated as spiritual versus natural. In other words Luther believes man has no spiritual free will. That is to say he, in the sinful state only has freedom to sin, and sin only within the circumstances that God has ordained for his life materially. However is does allow some freedom in the natural world, while either under the dominion of sin as an unbeliever, or under the power of the Spirit as a believer. Regardless of how man's will (or desire) is created by the Devil, or God, wether an unbeliever, or not, Luther allows 'some' natural freedom within the confines of destiny.

Or to put it in simple terms, here is what Luther allows with respect to a human's ability to have free will:

We know there are things free choice does by nature, such as eating, drinking, begetting, ruling, so that Diatribe cannot laugh us out of court with her shrewdly idiotic remark that if we press the word “nothing,” it would not be possible even to sin without Christ, although Luther has admitted that free choice avails only for sinning. (Luther's Works, Vol 33, Page 240)

He really says nothing more about the existence of human freedom in the entire book as the whole things was meant to argue against Erasmus' view of free will.