A ruling is the outcome of a court's decision, whether on some particular point of law (such as the admissibility of evidence) or on the case as a whole. A ruling may lead to an order--a court's written direction or determination, which may be either interlocutory (on an intermediate matter), or more broadly, final (and therefore dispositive of the entire case).
An opinion is a court's written statement of the relevant facts, the applicable points of law, the reasoning that led to the court's decision, and dicta, everything not directly germane to that reasoning. In British English, opinion may have this meaning, but the usual BrE equivalent is judgment [or judgement]. Instead, in BrE opinion typically refers to advice given by a barrister about the facts of a case or a legal memorandum prepared by a solicitor and given to the barrister.
A judgment is a court's final determination of the rights and obligations of the parties. It "includes a decree and any order from which an appeal lies." Fed. R. Civ. P. 54(a). Traditionally, a court of law renders a judgment.
A decree, traditionally, is a judgment rendered by a court of equity, admiralty, divorce, or probate. Today, the term judgment is more common in that sense, and decree refers more broadly to any court's grant of relief. The relief granted needn't be equitable in nature.
A verdict is returned by a jury, which decides whether the facts satisfy the elements of a claim or offense. The word is used loosely when a court reaches a decision in a nonjury trial--the better practice being to use verdict for juries only
From LawProse.org, Lesson #165 by Bryan A. Garner.