The one thing this novel has going for it is that it is a fairly effortless read likely to keep you turning the pages, though maybe not compulsively. In other words "Omerta" would be undemanding company for a long journey, or perhaps a stay with relatives you don't much like, but otherwise there is little to recommend it.
The basic idea is intriguing enough: the adopted son of a true, old school Sicilian Don (who has retired from crime) is raised secretly in the old Mafia ways so as to be one day capable of defending the family. The twist here is that the Don's three grownup biological kids, although quite capable and successful in their respective chosen careers, are respectable upright citizens almost entirely ignorant of their dad's "business". Could've been a great story, but sadly plot and characters are shallow and unconvincing, and inter-relationships between the main players are especially weakly drawn.
If you're unfamiliar with Puzo's work, I suggest you read "The Godfather" first, perhaps followed by "The Last Don". If you've already read those then ther's no earthly need to bother with "Omerta", it's a disappointing last bow from a great storyteller.