What is an overview of Christian beliefs regarding which spiritual gifts are still available to the body of Christ and which ones have ceased?

For a list of which gifts have generally ceased one would have to turn to a Cessationist. The only work I know that thoroughly delves into all the gifts and offices and delineates what he considers obviously ceased and which ones are not, is John Owen.

He basically considers any first century office not normal in all churches in history as temporary for the unique challenges at the time, these include: Apostles, Prophets and Evangelists.

I found it a little odd that he included Evangelists as we now consider this a very popular person – but we must remember that cessation of the extraordinary offices and gifts does not mean that there is not some similar gift remaining in normal church history.

But although all these gifts and operations ceased in some respect, some of them absolutely, and some of them as to the immediate manner of communication and degree of excellency; yet so far as the edification of the church was concerned in them, something that is analogous unto them was and is continued. He who gave “some apostles, and some prophets, and some evangelists,” gave also “some pastors and teachers.” And as he furnished the former with extraordinary gifts, so as far as any thing of the like kind is needful for the continual edification of the church, he bestows it on the latter also, as shall be declared.( Owen, J. (n.d.). The works of John Owen. (W. H. Goold, Ed.) (Vol. 4, p. 475). Edinburgh: T&T Clark.)

The kind of Evangelist that ceased, in Owen’s mind, were those who exercises miraculous gifts within their office, which made it unique. Actually he mentions four things associated with extraordinary offices:

There are four things which constitute an extraordinary officer in the church of God, and consequently are required in and do constitute an extraordinary office:—1. An extraordinary call unto an office, such as none other has or can have, by virtue of any law, order, or constitution whatever. 2. An extraordinary power communicated unto persons so called, enabling them to act what they are so called unto, wherein the essence of any office doth consist. 3. Extraordinary gifts for the exercise and discharge of that power. 4. Extraordinary employment as to its extent and measure, requiring extraordinary labour, travail, zeal, and self-denial. All these do and must concur in that office and unto those offices which we call extraordinary.( Owen, J. (n.d.). The works of John Owen. (W. H. Goold, Ed.) (Vol. 4, p. 439). Edinburgh: T&T Clark.)

Regarding the gifts that have ceased (at least in the same extraordinary manner), are listed in 1 Corinthians 12:

To one there is given through the Spirit a message of wisdom, to another a message of knowledge by means of the same Spirit, 9 to another faith by the same Spirit, to another gifts of healing by that one Spirit, 10 to another miraculous powers, to another prophecy, to another distinguishing between spirits, to another speaking in different kinds of tongues, r and to still another the interpretation of tongues.( 1 Co 12:8–10)

Again it is important to understand that Owen means these gifts had an unparalleled extraordinary use in ACTS and in the first century while the Apostles lived but that many of them in less powerful ways still maintain the church today. For example he specifically mentions Luther as someone who essentially had the gift of faith as it was an unusual and steady confidence to proclaim the gospel will almost the whole world against him – as the Apostle Paul. So even to a Cessationist, during critical parts of Christian history where unusual outpouring of the Spirit occurs, or as the situation of the church needs, God still gives gifts and they may be in some almost equal to the gospel times.

However these current versions, in Owen's mind are not extra ordinary, for example the wisdom and discernment that the Spirit may give us in a time of need. An uneducated fisherman might not suddenly have enough wisdom to confound the best of Greek Philosophers in an astonishing Biblical display of wonder, yet a persons wisdom as given by the Spirit today in a church may still be highly remarkable and noticed by all. Those obvious miracles things like healing without doctors and miraculous signs, etc. Owen sees as having no real similar gift in the rest of Christian history, mostly because other than a few weirdos, nobody even claims to have had them. For example when speaking about an extraordinary miraculous discernment, he writes:

And whereas the communication of these gifts is ceased, and consequently all pretences unto them, unless by some persons phrenetical and enthusiastical, whose madness is manifest to all, there is no need of the continuance of this gift of “discerning of spirits;” that standing infallible rule of the word, and ordinary assistance of the Spirit, being every way sufficient for our preservation in the truth, unless we give up ourselves to the conduct of corrupt lusts, pride, self-conceit, carnal interest, passions, and temptations, which ruin the souls of men. (Owen, J. (n.d.). The works of John Owen. (W. H. Goold, Ed.) (Vol. 4, p. 472). Edinburgh: T&T Clark.)

This is somewhat ironic that Owen regards extraordinary 'wisdom and discernment' to have also ceased because many reformed believers think Owen was one of the most wise and discerning theologians in history. But I think we can understand his meaning. So maybe we should say current gifts are not 'extra-extra-ordinary' as Owens gifts are extra ordinary when compared to most.

Of course, this is nothing new. Moses had extra miraculous gifts and then hundreds of years went by with little mention of similar miracles during the prophets. At least nowhere near to the same frequency in one man’s ministry. Then when Jesus was on the earth, his own ministry is filled with numerous miracles. Also, the miracles in the New Testament were the kind that people could not deny. Imagine someone healing a hundred war veterans with missing limbs, by giving them new ones! Many would come to believe. Today the fake healers always do healings that can’t be verified and for those that claim to have been cured of cancer one month, are followed up by some, and its surprisingly has returned. Then the faith healers blame them for their ‘lack of faith’ to ‘keep the healing’. This kind of ministry has no similarity to the ones in the Bible.

Miracles can occur when God wills them, and they are not easily denied. God would not waste overwhelming human faculties to the demonstration of his power if they could be denied so easily.