I think his best points & ironies come in the short stories. Any of the volumes would do. I think that's generally true in Yiddish literature - like jokes, maybe - short & sweet. But don't stop there. Aleichem is the best known/best loved of the lot (and deservedly so) but partly because he was mostly light & easy. You can truly be staggered by some of the others. They get further into religion, mysticism, social values (rarely politics as such). The stetl was such a life in micrososm. Even demonology. But mostly the arbitrariness of life we often see in folk material but rarely in our world-wide Protestant-Ethic society. Folk tales know the Good, hard worker, honorable people don't always "win." Disney tells us they do.

Even when these stories leak over into Europe & America they retain the quality. Usually. Singer, of course, but also Singer, Peretz, Asch, etc. Strongly recommend A treasury of Yiddish stories,
Howe, Irving, ed.; Greenberg, Eliezer, Publication: New York, Viking Press, 1954 (& reprints)

When I was substitute teaching high school in New Orleans in 1966 and had been left no lesson plan or clue where to continue the regular work (or those many classes that just had no regular work - truly rotton school system - I'd read a shorter story from that book & we'd Discuss. It was amazing how universal the stories were. Or maybe there was some wider appeal to the disenfranchised...