Russell's prose is unusual -- almost lyrical -- and the imagery she uses is very strange, but I think I might love her. I've certainly never read anything like her before, and in a saturated market, you can't beat good, old-fashioned creativity.
Cute as it is, reducing Russell's book to this list of "noxiously fanciful" oddities, even for the purpose of proving a point before going on to shower the book with praise, which the NYT article does, does her a disservice.
Certainly, the aforementioned images and characters appear in Swamplandia!, but they're not what the book is about. Not even a little bit. The book is about a grieving family, recovering from the loss of their matriarch while trying to deal with financial ruin and teenage growing pains.
At it's heart, this is universal stuff.
For all the talk about the strangeness of Russell's settings, her story is ultimately about a very average family. They simply happen to live in very unusual circumstances. The "Bigtrees" live on the fringe. They're island-dwellers who home-school their children (and the children are, as a result, seriously unsocialized). But the drama of the story grows out of loss, grief, poverty and assimilation. It's a book about things you know, wrapped in a shell of things you are unfamiliar with (say, the alligator wrestling) and the result is extremely compelling, and very, very sad. (Look out for very serious stuff such as possible suicide attempts and rape.)
I really don't want to give too much away except to say that the impression I got from this book was similar to what I felt while reading Peter Rock's My Abandonment (which I raved about last year). If you read that book and liked it, I highly recommend you read this.
I started with the novel because it's the book I was given first, but it might have been better to begin with the 2006 short story collection, St. Lucy's Home for Girls Raised By Wolves. The stories will give you a good idea of Russell's style and you won't have to commit to a longer piece. Also, St. Lucy's contains a prototype or seed story that seems to have germinated into Swamplandia! as a whole, so that's another good reason to read it first. (The story won't be as compelling if you read it after getting to know the same characters in the longer novel.)