この話はおかしくない(か) I'm not positive but this looks to me like something you'd say after introducing the story. I'm not sure you can use it without a referent for 'kono,' what is 'this' before actually telling it ?
'Nani ka okashii hanashi ha nai no ka' I think I've seen somewhere (as a sample sentence in the goo dictionary) for "Isn't this something funny/strange" but I can't find it at the moment...They probably just left off "Kore wa" as the subject.