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There is a device that often appears in Hebrew writings known as chiastic structure. Essentially it extends chiasmus (a common literary device that relates clauses in criss-cross fashion—think "the first shall be last and the last shall be first") to an entire passage. It is particularly common in Old Testament writing. Another word used to mean chiastic structure is palistrophe.

For example, a palistrophe or chiastic structure may have the form ABCDEDCBA, meaning that an idea A is presented, followed by an idea B, and so on. Thus the first idea presented is also the last. Other chiastic structures are possible, but they are still structured so that the first and last ideas are the same (or, at the very least, similar).

I think chiastic structure appropriately describes what you are seeking.

Added: a link to a picture of the chiastic structure of Genesis 6–9 for reference.

You'd talk about the father's side and mother's side separately. (Credit @JoshRagem's half-uncle / half-nephew idea.)

Consider Gary.

• Father's side: trace the relationship through Andy. Harry is the son of Gary's half-brother. So Harry is Gary's (half-) nephew on his (Gary's) father's side.

• Mother's side: trace the relationship through Fanny. Harry is Fanny's half-brother. So Harry is Gary's (half-)uncle on his mother's side.

An uncle is the brother, half-brother, step-brother, or brother-in-law of one's parent, or the husband of one's aunt. - wikipedia

So Harry is Gary's paternal (half-)nephew on his father's side and (half-)uncle on his mother's side.

Correspondingly, Gary is Harry's (half-)nephew on his mother's side and (half-)uncle on his father's side.