He is biting his toenails (like someone would bite their fingernails but worse). That's the joke. His wife accuses him of being disgusting. He finds this accusation surprising even though he is doing a really disgusting thing at the time.

Hi Yuan, Yes, it is a very strange thing to say, isn't it? I've never heard that particular expression before, and it certainly isn't a well known idiom in American English. It seems that the speaker is trying to convey his utter surprise at his wife's extreme reaction to his habit of being unorganized and unclean. Perhaps choking on toenails means that something form way down below was brought up for him to symbolically choke on; I doubt he was literally sucking on his toes. I would need more context, perhaps, to determine what he means, exactly.