As a native of America, I will say that most speakers are not good examples of what constitutes correct usage (although it exactly constitutes popular usage). Also, citing occurrence statistics does not provide any clarity, meaning, or value, since you are citing the usage statistics or words that are not synonyms.
Here is how I would attempt to explain the difference.
Here is an example that supports this view (from "The Six Labors of Father Vilmer" by Garrison Keillor):
Without looking down he slowly climbed up under the first light, reached up, took hold of it, and twisted it out. Then he moved the ladder, looked up, saw it still swaying up there, and bravely climbed again. He stretched way up and pulled out the second light. He moved the ladder again, and again and again, got the third, the fourth, the fifth light. As he started up the sixth time [the last light], he looked up all those rungs and prayed, “O Lord, please don’t be ironical. If you wanted me to fall, it should have been on the first one!”
ironicalmust be word sinceironicallyis a word, whereasironiclyis not. This also supports my previous claim since an object which only indirectly has irony (like the novel) does not directly do something in an ironical manner. Only the specific sentence says something ironically. – stevendesu Nov 14 '10 at 17:35