In this context, jiken (事件) means "incident" or "case".
The full picture indicates tamago jiken which literally means "the egg incident" where a chick is killed due to the egg getting cracked.
There might not be any deeper meaning considering Oda's nature of humor.
EDIT: Rarely. 百合 is more common. The other two seem to be A) part of people's names or B) Lily flowers.
A few searches on google, amazon or any eshop will give you a rough idea.
Just a language note, any word in Hiragana can be written in Katakana. Katakana can be used for emphasis or italics purposes (often loan words but not necessarily).