While I was reading this, I couldn't help but compare it to Laurence Sterne's "Life and Opinions of Tristram Shandy." I later found out that Gogol was a fan of that book, so perhaps the parallels are intentional.
The protagonist, Chichikov, is a shaggy dog of sorts an average guy from a below-average background, who manages to use his schmoozing skills to get ahead in life, but is ultimately a bit of an insecure charlatan. (Lots of parallels to Jay Gatsby as well.) But, as in Sterne's book, we don't find out much about Chichikov until the very end of the novel -- otherwise, we only see small glimpses of Chichikov in action, and hear the mostly untrue things said about him by those he encounters. (Are these falsehoods of his own making, or of his observers' making? Or of ours, the readers' own making? Not an easy question.)
The novel takes us through various parts of Russian society, with many bits of the author's mockery obviously being things Gogol had wanted to get off his chest for quite a while. There are some excellent observations about "the Russian character," human nature, personality types, what different languages are good for, and many, many other bits of Gogolian brilliance. By the way, the financial scheme Chichikov is running is very clever, even by today's standards of financial wizardry.
The narrator does a lot of Sterne-like "stepping out of character"; in one of the more hilarious passages, he complains that his pen has suddenly become too heavy to write anything more about a certain character, and that he will take a rest. There are many comments to the effect of "So what kind of a novel were you expecting this to be, dear reader?" perhaps playing upon the shock with which the book was initially received. Also lots of teasing the reader, with back-and-forth to the effect of "should I reveal any more to you, or shouldn't I?"
Ultimately, the big question in the book becomes exactly who the "dead souls" are -- and the astute reader will realize that paradoxically, the dead serfs that are being bought and sold are the least dead of all the souls in the book.
This book is hilariously funny, and is rewarding even if read for humor alone. However, the literary and narrative experiments it undertakes, as well as its subtle social criticisms, make it even more worthwhile.