Ironical is a variant of ironic. It has no definitions of its own. Ironical was once preferred to ironic (see the Ngram at the bottom of this post), but ironic now prevails by an overwhelming margin.
Examples
There’s no reason why ironical should not be changed to the standard ironic in these sentences:
Obviously the show is well regarded and it is in a prestigious gallery, but it is meaningful only to those prepared to play the game of ironical banality. [New Zealand Herald]
She does occasionally scold him, but in a safely ironical way … [New Yorker]
The Free World is an episodic chronicle, delivered in an understated style which can accommodate serious subtexts as well as ironical humour … [Independent]
Because the suffix conventions in English are inconsistent, ironical will probably continue to appear. For example, metaphorical is preferred over metaphoric, academic and seismic are preferred over academical and seismical, and economic and economical are both legitimate words with different meanings. Because there are no simple, consistent rules for these suffixes, and because spell-check approves of ironical, the word will continue to appear. And perhaps someday it will find a meaning of its own.
Ngrams
The following Ngram charts the use of ironic and ironical in English-language books published from 1800 to 2000. It shows that ironic took over in the 1930s and has never looked back.
