Efficacy in the context of war means one thing: does it accomplish the objectives, does it complete or accomplish the mission? A complete mission is the accomplishment of one or more objectives, usually at some material and human cost to those undertaking the mission. An accomplished mission is one where all objectives are fulfilled at projected or minimal cost in both material and casualties to the friendly side.
An exhaustive examination of commando units, special warfare, and irregular units during WW2 is easily the subject for an entire Master's thesis or Doctoral dissertation and is beyond the scope of AskHistorians. However, we can examine a few of the most effective units fighting for the Allies. Since your question was aimed at Allied units, I will cover the activities of the Allies. You are welcome to ask more specific follow-up questions about the Soviet and Axis powers and I and others will try to answer those as well.
An Overview in Brief
Both the Axis, Allied, and Soviet military machines used special forces. All of them are the precursors in some way to the elite units utilized by modern governments. Each of them are designed around similar objective fulfillment. Similar to regular units, elite units are trained to be diverse jacks-of-all-trades with a wide military education. However, the education of an elite unit is much more thorough. They almost always have exceptional performance as a regular battlefield soldier and excel at both classroom learning and practical hands-on education. They are quick learners, ideologically pure (that is, true believers sometimes to a fault in the justice of their cause), and are expected to act on their own recognizance in fulfillment of orders. Sometimes, this means not adhering to regular rules of engagement (do not fire unless fired upon) and utilize without discrimination or hesitancy what we would now easily call "terror tactics". In fact, the tactics utilized by all the jihadist groups are only slight modifications of what was taught to them by both Soviet and Allied forces during the War in Afghanistan in the 1970s and firmly have a place familiar to the irregular warfare of all sides during the Second World War.
It is helpful to differentiate between WW2 factions as they were known in the time period. "The Allies" refers to the coordinated effort of British and American militaries and the governments-in-exile belonging to France, Poland, and other Allied nations. "The Axis" refers to the coordinated effort of Germany, Italy, Imperial Japan and their client states. "The Soviets" refers to the USSR, which did not wholly coordinate with the Allies but acted according to their own objectives in concert with the Allies where it was beneficial to both parties.
What were the objectives of special units? In almost every mission they were deployed, they were to gather information and sabotage the enemy in preparation for an invasion or attack by regular forces. In some cases, they acted directly as counterintelligence, spreading false information to delay or mislead the enemy and sabotage their own special forces activity. Within friendly territory, special forces were utilized as secret police against the resistance of the civilian population and all sides engaged in this kind of activity in the mindset of "total war"; that is, the civilian population is part of the war machine and are just as capable as a regular soldier of acting against the objectives of an occupying force.
On all sides, the actual activity of special forces relied on a fantastically gigantic war machine. Their budgets only grew as the war progressed. Very rarely did a single individual act alone on a mission, and only then with heavy friendly support; individuals that were deployed alone almost always volunteered for the mission and were frankly considered crazy by some.
For every special forces unit that was deployed in action, millions of dollars went into their operations in terms of logistics, war material, preliminary intelligence gathering, and more. We can meaningfully divide special forces units into three distinct categories depending on the objectives they were assigned: commandos, spies, and agitators. Commandos are units acting in a direct military capacity and were assigned to military and infrastructure objectives; their goal was to blow up, destroy, assassinate, and terrorize. Spies often appeared as civilians with no clear indication they were part of a regular military unit; their job was to gather intelligence, spread misinformation, and sometimes act on their own recognizance to take out targets of opportunity. Agitators were deployed to areas where there was active resistance to an occupying force, train that resistance and establish a clear link of funding and communication with a sponsoring government, and act as a fifth column military force in coordinated action with their sponsor. All of these tactics became the de facto way that the Cold War was waged later from 1946 to 1991.
All in all, special forces did what regular military units could not, but regular military units accomplished objectives that special forces alone never could.
Jews served in military special forces capacity in numbers disproportionate to their population, which means that Jews overwhelmingly volunteered to risk their own lives to fight the Holocaust. I seek to illustrate this below and emphatically declare the death of the myth that "Jews did not fight back and only waited for a Messiah that never came". The whole of Israel served as their own suffering servant and Messiah. Without Jewish participation in the war, the war would have been lost for the Allies.
The Allies
The Office of Strategic Services or OSS was the irregular warfare unit of the United States and the direct precursor to the modern Central Intelligence Agency. It was headed by Major General William Joseph Donovan and Brigadier General John Magruder. They acted in an unofficial capacity from July 1941 and in an official capacity from June 1942 to the end of the War and beyond as the CIA. They innovated what we might now think of as "spy gadgets" and were responsible for everything from blowing up rail lines to faking entire military units to gathering insane quantities of information. I do not use the word insane lightly; what they were doing then was unprecedented in scale if not in quality, and the sheer quantity of information they gathered on Axis activities was truly staggering. Entire warehouses were filled with OSS data and they had a small army of secretaries and personnel with security clearances who's sole job it was to collate and analyse this information. The sheer quantity of data made it very easy for some data to occasionally be leaked or handed over by moles (a mole is a person actively controlled by the enemy side to act on their own recognizance per orders given by their controlling government), or otherwise be copied or "go missing" entirely.
Whereas the USA provided the machine and personnel, much of the intelligence and training came from Britain's British Security Co-Ordination (BSC). Together as a coordinated single entity, these offices conducted operations in neutral countries such as Iceland, Sweden, and Switzerland. In the latter, OSS and BSC activity infamously revealed Swiss complacency regarding Third Reich financing and even facilitating the movement of Nazi forces through their territory, leading to an Allied bombing campaign against Switzerland, but of course the country was never invaded and a post-war examination exhonerated the Swiss as acting in the interest of their own self preservation. That is, they didn't have much of a choice in the matter and trying to fight as a member of the Allies might have led to the complete extinction of the Swiss people as a whole.
Some of the most effective activities of the OSS include supporting the French Resistance in both occupied Northern France and facilitating the 1944 invasion of Vichy France. They sabotaged Italian and Nazi forces in the North Africa campaign. They funded anarchists in Fascist Italy who terrorized the Blackshirts in concert with the naval and land invasion of the country from North Africa. They trained the Chinese Nationalists in irregular warfare and subsequently expelled the Japanese from Manchuria.