Here are three thoughts on speaking about judgement. These aren't the three most important things to say but they are the three things I think we're commonly getting wrong.
1) Our job is not to save God from the 'guilty' verdict.
So often I hear talks that seem to aim at getting God off of our "guilty" verdict rather than getting us off of His. If you aim at trying to save your hearers you'll present God righteously. If you aim at justifying God, you'll save neither.
2) We don't bring hell to the world, hell is here. We bring reality and then hope.
According to Romans 1, the wrath of God is being revealed from heaven. All that sinful humanity chooses is already hell-bent. This means that earth's vision of heaven is heaven's vision of hell. As we herald heaven's vision, we're not saying 'Ah, life is rosy now but the pit awaits.' We say 'Don't you realise how life is the pits now? Don't you realise we've already fallen? Don't you see where this thing is already heading? Don't you want a way out?' In this way we don't introduce hell to people who are otherwise living it up. We point to the hell in our hearts and the hell in our world and say "Hell is here and it needs nipping in the bud before it goes viral. But we know Someone who takes it seriously. Jesus can handle your hell and give you His heaven."
3) The quintessence of hell is not sin's recompense so much as mercy's refusal.
It's fairly common to do a 'reverse Godwin' when speaking of judgement. We begin with Hitler and the justice of judging him, then we work backwards towards less flagrant sinners... like ourselves. I wonder though if that frames everything in terms of degrees of just punishment, and while there's a place for that I think leaning too heavily on this will come a cropper in the face of eternity. (You can tell people 'temporal sins against an infinite God = eternal punishment, QED" but I've never seen it convince anyone.)
Luke 15 finishes with the bad boy in the feast and the good boy outside, with weeping and wailing and the angry gnashing of teeth. This is pretty much every way Jesus describes hell in Luke's Gospel, but the question comes: Why is he there? Because he's so bad? No, because he's so good - too good for this mercy meal. Why is he shut out of the feast? Because his father is so cruel? No he's so kind - too kind for this moralist who insists on justice.
In Luke 15 "justice forever" is the motto of hell's inmate, not its Jailer. If we let shared concepts of "justice" do all the heavy lifting on this question it frames God's ultimate posture towards the world in terms of law. But what of the "wrath of the Lamb"? The anger of the spurned Lover? Is there an evangelical (and not merely legal) preaching of hell? Or do we always come back to a law which the New Testament says has been fulfilled by Christ (the curse and all)?
Similarly I worry that an exclusive focus on the justice perspective obscures, not only the gospel character of God but also the mad mystery of human iniquity. As we hear of Matthew 25's goats, certainly we're meant to think that their punishment is fitting, right and even that there is a poetic justice to it all. But we're also meant to think 'That's insane! Goats: hell is not for you! It's for the devil and his angels. Why are you following him!? Why won't you turn and live, for who can take any pleasure in your perishing?!' God certainly doesn't (Ezekiel 18:30-32).
Our preaching of hell should lead to a gospel appeal from the depths of God's own heart, not an 'all-sewed-up' accounting for sin's recompense. That's what I mean by an evangelical (and not merely legal) account of hell.
If you want a terrific example of preaching hell, check out Steve Levy: