Perhaps the four-line poem can be thought of as the artistic equivalent, in English, of the Japanese haiku. A haiku consists of 17 syllables written in three lines (although it can be written in one line). I know just enough Japanese to be dangerous. However, I am going to go out on a limb and suggest that Japanese is more concise than English. A great deal more can be accomplished in 17 Japanese syllables than in 17 English syllables. Hence, English speakers need one more line, and many more syllables, than the Japanese do to create a memorable short poem.
The following poem by James Reeves has been a favorite of mine for a couple of decades. It becomes more resonant (and more insistent) with each passing year.
Terrick Williams, "Quiet Night, Honfleur" (c. 1922)
Things to Come
The shadow of a fat man in the moonlight
Precedes me on the road down which I go;
And should I turn and run, he would pursue me:
This is the man whom I must get to know.
James Reeves, The Questioning Tiger (1964).
Now, I am not about to suggest that there is a "formula" for a successful four-line poem. But one thing is clear: the poet must get to the point. Staying away from adjectives is a good idea. Precise images are also a good idea.
As one might expect, the fourth line is crucial. I would not say that it has to contain a surprise or a twist. Nor would I say that it has to tie things up neatly. In poetry, ineffability -- as opposed to obscurity -- is always a good thing. I never like to begin a sentence: This poem is about . . .
But I would say that the final line should, while being of a piece with the first three lines, make a turn (I cannot come up with a better word at the moment) that causes a "click" in the reader. The "click" is, yes, ineffable.
Thomas Train (1890-1978), "Headlights"