A GREAT question. Your question actually describes a project that I have been working on for some time now (described at the end of this answer).
To answer your question simply: think of Jesus as a great entertainer, a great storyteller, and amusing speaker. He was not a preacher or a “holy” man in the sense of a Dali Lama. Nor was he a “fire and brimstone” preacher, which seems to have been more the role of John the Baptist.
If the Sermon on the Mount, our most complete example of his work, is a good example, his first goal was often to get people interested, get involved. He started by surprising them. He would make light of very serious subjects (poverty, death, etc.) but in interesting ways. He won them over by getting them laughing. After that, he wanted to get them thinking. But he continually moved back and forth between the serious and clearly more entertaining material.
Of course, most of this is lost in our modern translations, which focus on a very sanctified version of what he said. Modern translations are more interested in making theological points than entertaining us or capturing the personality of Jesus. The problem with that approach is that it makes a lot of what he said sound very strange to modern ears.
For example, he often used exaggeration to entertain people, as any good comedian today would do. Cutting off limbs. Plucking out eyeballs. If you go through his words, you can see that many were chosen because he could act them out. If you imagine them being acted out, they are quite funny, even silly. For more on this topic, including a number of examples, you may want to read this article on Jesus’s Humor.
The answer specifically about phrases like “The king was enraged. He sent his army and destroyed those murderers, and burned their city”, or, “The king handed the man to the jailers to be tortured”? Imagine a story-teller reading children stories about dragons and witches coming to their demise. That is what Christ was doing, exactly.
I am working on versions of all of the major “speeches” in Matthew that captured the entertainment value of the original Greek, including what I imagine (based on the Greek words) was his tone, actions, interactions with the audience, and the questions that he was responding to when he spoke. And, yes, we know that much of what he said was in response to unrecorded questions. In the Greek, we can see when he goes from addressing the crowd (a plural you) to an individual (a singular you). This, of course, is impossible to see in English.
I may be getting close to finishing a version of the Sermon on the Mount. If anyone is interested in seeing it, you can ask me on Quora and I will upload and provide a link.