The example you have given is not described by any of the terms on your list. "It's all in the family but with no relation" is actual an example of a kind of irony. We can also say that this phrase is exhibiting figurative language.
Figurative language describes a purposeful use of language where the denotative meaning of the terms, phrases, words, etc., does not apply. Figurative language, in other words, is not meant to be taken literally. In your example the "family" is a figure of speech, not a literal family.
There are two ways to read the term "family" in your example, which is why this is a case of irony. Irony results from the presence of two meanings (or more) in relation to a single circumstance. Your example uses the type of irony known as verbal irony.
Verbal irony is a disparity of expression and intention: when a speaker says one thing but means another, or when a literal meaning is contrary to its intended effect.
Verbal and situational irony are often used for emphasis in the assertion of a truth.
Here "family" is being used initially to suggest that there is a bond of blood then comes to be seen as a different kind of bond, a bloodless bond, as it were. "Family" takes on two meanings and so becomes ironic.