The scholarship on this era in Soviet espionage largely regards Hiss' guilt as a settled matter. Venona cable #1822, released in the 1990s, is often seen as the final nail in his coffin. In the cable, sent on 3 March 1945, the Soviet rezidentura in the US reports that the agent codenamed ALES had attended the Yalta conference, and then travelled on to Moscow — a description which precisely fits Hiss' movements in January/February 1945. That, coupled with other evidence from documents and defectors (all circumstantial in isolation, but compelling in aggregate) have led most intelligence historians since the Venona releases in the 1990s to largely take as read that Hiss was a spy:

• Allen Weinstein, one of the premier authors on the Hiss case (and initially a believer in Hiss' innocence), published a pair of works that conclude Hiss was a spy — first Perjury: The Hiss-Chambers Case and later The Haunted Wood. Weinstein is the bête noire of the pro-Hiss camp, and much ink has been spilled challenging his work — too much to even begin summarising here.
• Christopher Andrew notes in The Sword and the Shield that “The corroborative evidence now available puts [the identification of Hiss as ALES] beyond reasonable doubt.”
• Richard Aldrich writes in his history of GCHQ that Venona "helped to resolve some of the most bitterly contested Cold War espionage cases. These include the famously controversial cases of the atomic scientist Julius Rosenberg and the diplomat Alger Hiss, who were both active espionage agents for the Soviets.”
• in Spies: The Rise and Fall of the KGB in America, John Earl Haynes and Harvey Klehr felt sufficiently confident to title the book's opening chapter 'Alger Hiss: Case Closed'.
• in the most recently published history of Soviet intelligence, Jonathan Haslam doesn't even acknowledge any lingering doubt; he simply describes Hiss as a "former diplomat and GRU agent”.

Hiss lawyer and scholar John Lowenthal was for many years the preeminent voice speaking out for Hiss' innocence — you can find him making his case that Hiss was not ALES at length here. As you might have guessed, I don't find his evidence especially persuasive.

Hiss, in my mind, is just the most prominent of a brace of prominent American officials accused of spying for the Soviets in the 1930s and 1940s, who were essentially tried in the court of public opinion during the Red Scare — and for many, the prosecution case was found wanting. But with the vast reams of new archival material that have landed in the laps of intelligence historians since the end of the Cold War, some of those cases are now fairly readily closed. I think Hiss is one of those. Harry Dexter White is another; I've never heard a particularly credible case made against Oppenheimer, however.

Venona does not indicate Oppenheimer was a spy. It indicates that at one point they considered him someone to perhaps be pursued, but there is no evidence that he was actually an agent of any sort.

Venona can be tricky on at least two fronts. One is attribution of code-names — it is easy to get those wrong in many cases, and in the past many historians have attributed them incorrectly. The cables rarely reference someone by their actual name, and when they do, it usually means they are unimportant — they used code-names (ALES, LIBERAL, ANTENNAE, CHARLES, REST, GOOSE, MLAD, etc.) to refer to actual agents/moles in the field. Sometimes you can figure out from context who they are, correlating them with information outside the cables (i.e. CHARLES/REST was a British scientist at Los Alamos with a sister in Cambridge, Mass. — that allowed the FBI to narrow him down to Klaus Fuchs, a task made much easier by the fact that there were only a few dozen British scientists on the project). But there are cases where it is quite tricky.

The other is the fact that the information itself may not always be accurate — some of the Soviet agents exaggerated their recruiting work in order to avoid being recalled to Moscow (and executed) for inactivity. The Venona transcripts can be tricky to deal with for these two reasons, along with the fact that they are not complete (even individual messages can be missing portions, much less the messages that are missing), and the original Russian is unavailable to historians today (so we are relying on the NSA's translations).

As for Hiss — I am not an expert on the Hiss scholarship. My understanding is that the scholarly view is that Venona is thought by many to likely indicate Hiss was a spy, but that there are many areas of uncertainty in the attribution of the codename that is allegedly Hiss (ALES) to Hiss himself.