Stanza 4 Summary

Get out the microscope, because we’re going through this poem line-by-line.

There was a king reigned in the East:
There, when kings will sit to feast,

Whoa! All of a sudden Terence switches gears… completely. He's made his point about the value of poetry by explaining it directly (basically, life is sad, so we need sad poems).
Now he tries another strategy. He spends the rest of the poem telling a story about a king in the East. He's starting to spin out another analogy, explaining why we need sad poems by telling us this fable. Here he begins by talking about feasting, which makes sense, because that's definitely something kings are into, right?

They get their fill before they think
With poisoned meat and poisoned drink.

Bummer. Since feasting was all the rage, apparently poisoning was a big problem for kings in the East. People who wanted to get rid of them would pack their food and drink with poison. Worst. Feast. Ever.

He gathered all that springs to birth
From the many-venomed earth;

But this crafty king has a plan to stay safe. He gathers up all the poisons that arise ("spring to birth") from the earth. "Many-venomed" just means full of different kinds of poisons.

First a little, thence to more,
He sampled all her killing store;

Then, weirdly, he starts to eat or "sample" these poisons. He starts small, then builds up from there, until he's tried the whole supply of poisons (the "killing store") that the earth produces.
Notice the subtle personification when he refers to the earth as "her." Making the earth a girl is a pretty common poetic move, but we think it's a little creepier when "she" is making poison. The earth is supposed to be our mother, right? Well, it fits right in with Terence's gloomy vision of the world.

And easy, smiling, seasoned sound,
Sate the king when healths went round.

Thanks to his training, the king doesn't have to worry about poison. When there are toasts (Housman uses the word "healths") at the dinner table (usually a great chance to poison someone), he's just fine.
Rather than being freaked out about poison, he's "easy" (relaxed), smiling, "seasoned" (experienced, well trained), and "sound" (healthy, secure). The dude is totally chilled out.

They put arsenic in his meat
And stared aghast to watch him eat;

Apparently the creeps whom the king eats with want to kill him. To do that, they put arsenic (a deadly poison) in his meat, and then sit there watching him in horror ("aghast").

They poured strychnine in his cup
And shook to see him drink it up:

In case arsenic didn't do the trick, the jerks at the king's feast try a little strychnine (another nasty poison, often used to kill rats) in his drink. Then they wait, trembling, for him to drink and die.

They shook, they stared as white's their shirt:
Them it was their poison hurt.

These creepy dinner guests tremble and shake and stare, turning as pale as their own shirts. In the end, though, they are the ones who are poisoned ("hurt") by the arsenic and strychnine they put in the food.
And why is that? Well, it turns out the king is immune, because he sampled all those poisons bit by bit, and built up a resistance. This is a lot like the trick that Wesley uses with iocane powder in The Princess Bride.

—I tell the tale that I heard told.
Mithridates, he died old.

The king, whose name turns out to be Mithridates, lived to a ripe old age, at least according to the fable that Terence heard. (Fun fact: the process of gradually making yourself immune to poison by consuming small amounts is called mithridatism, after this ancient king.)
So what's the point of telling this kind of long and seemingly unrelated story at the end of this poem? Well, the allusion to this ancient legend is an analogy for the benefits of poetry.
If you drink up a little sadness in small doses through poems, then maybe the major sadness of life won't kill you. You're sure to run into trouble sooner or later, so you should be prepared, and Terence thinks that poems can help you with that. That's the final answer that Terence gives to his drunken friend. What's the use of sad poems? To help you survive the brutal sadness of life. Sure, it's a little pessimistic, but maybe Terence is onto something, too.