The fact that the word ‘gehenna’ is used in later Jewish apocalyptic and rabbinic writings is of limited significance. It is, of course, possible that they reflect earlier traditions that would have been alive in the first part of the first century. According to Jeremias the earliest Rabbinic reference is in T. Sanh. 13.3, though it is always questionable whether these represent genuinely early traditions:

The School of Shammai say: There are three classes; one for EVERLASTING LIFE, another for SHAME AND EVERLASTING CONTEMPT who are accounted wholly wicked, and a third class who go down to Gehenna, where they scream and again come up and receive healing, as it is written: AND I WILL BRING THE THIRD PART THROUGH THE FIRE, AND WILL REFINE THEM AS SILVER IS REFINED, AND WILL TRY THEM AS GOLD IS TRIED; AND THEY SHALL CALL ON MY NAME AND I WILL BE THEIR GOD.

But the question is whether there is good reason to think that Jesus’ use of the term presupposes the same literary and theological context. There is little in the Gospels to suggest that he spoke and thought like the Rabbis (or the later apocalypticists) and much to suggest that he spoke and thought and acted like the Old Testament prophets.

So my argument would be that Jeremiah 7:30-33; 19:1-13 provides the most relevant interpretive context for Jesus’ notion of a judgment of gehenna. Just as the words in the temple about making it a ‘den of robbers’ are intended to recall Jeremiah’s warning that God will destroy the temple because of the sin of the people (Jer. 7:8-15), so Jesus deliberately invokes Jeremiah’s appalling vision of the dead thrown into the valley of Hinnom during the Babylonian siege of Jerusalem. He does so because he believes that Israel is on a path that will sooner or later lead to the military destruction of Jerusalem.

I have just posted some comments on Luke 12:4-5; Matthew 10:28 is discussed here.

Why is having one’s corpse be cast into that valley any more terrible than being unceremoniously cast anywhere else? Something more seems to be going on.

Yes, something more is going on. The point about the corpse being thrown into the valley is that it symbolizes God’s devastating judgment on his people. It is not simply death and lack of burial that is at issue here; it is the horror of God’s rejection of his people.

Since everybody dies—and in ancient times that was often at a young age—the disaster of AD 70 seems inadequate to explain the severity of Jesus’ warnings about avoiding Gehenna—that it is better to pluck out one’s eye or cut off one’s hand than to be cast into Gehenna (Matt 5:29-30). This is especially so in that most of his audience would be dead before AD 70 some forty years later.

I think this simply misunderstands the force of the prophetic witness. The primary concern is not with the fate of any particular individual (that is our modern, post-enlightenment perspective) but with the fate of the holy city, the place of God’s dwelling, and of the nation. The warnings are directed against the ‘evil and adulterous generation’ that rejects the Way of hope and survival, and whose behaviour will within a generation bring the destruction of war upon itself. It seems to me that the jeopardy that Israel was in fully accounts for the severity of Jesus’ language. Not only Jesus but also Josephus described the war as a time of unprecedented suffering for Israel: ‘the misfortunes of all nations since the world began fall short of those of the Jews’ (War Proem 4; cf. Matt. 24:21-22). Wouldn’t it be worth losing an eye or a hand to avoid that outcome?

On the face of it James 3:6 is a more general statement and may reflect a different conceptuality. But James, nevertheless, writing from Jerusalem presumably, foresees a coming judgment on the wealthy and corrupt that his readers will in some sense have to endure (5:1-11; cf. 1:2-4, 12). It doesn’t seem to me too difficult to locate James’ eschatology within the prophetic narrative of judgment and renewal that shaped Jesus’ teaching. If the tongue is set on fire by Gehenna, it is because it promotes the wickedness and conflict that will eventually bring judgment upon Israel.