First, civil law has, confusingly, two meanings. It can denote the legal systems used in most of Europe, as opposed to the common-law systems arising in England and spreading to most of the former British empire.
In the US, and in other common-law jurisdictions, civil law is pretty much everything other than criminal law. Given the tagging of the question, this seems to be the sense that you have in mind.
What is tort law and how does it differ from civil law? Is there any difference or overlap between the two? Does one more broadly encompass the other?
Tort law is a subset of civil law.
Are torts defined in statute?
Some are; some aren't. There is a common-law doctrine of torts. These torts have been defined by the courts through judicial precedent rather than by the legislature through statute law. They are therefore known as "common law torts." Some jurisdictions have abolished these torts and replaced them with torts defined by statute.
or do they exist alongside statute in some way more fundamentally and less ephemerally than statutes exist?
Statutorily defined torts are rather less ephemeral than common-law torts, not more.
What is a “common law tort “?