Clearly you've got a more strict definition of what you consider ironic than Alanis and I do. The things you listed as being "not ironic" are things that I would generally say were ironic. By what I thought was the generally accepted use of the word, not by the dictionary definition.

You're picking nits in a couple of places, like the line about the man dying after he wins the lottery; it's ironic to die after winning a huge prize therefore not being able to enjoy it, regardless of age. Although I admit, the line about good advice is a stretch but I think it makes a good rhyme in the chorus and brings the song together nicely.

So what other word would you use to describe situations like that? Where there's something darkly humorous about it, where you get the feeling that the universe is playing a joke on you?