Greetings! A most interesting inquiry within that question of yours. Allow me to attempt to shed some light on the situation. Note that it is somewhat hard to pinpoint exactly what you mean by communications (i.e diplomatic missions, military matters, or even something far less important such as trade deals), but I shall go ahead and deal with your suggestions one by one.
Iran: You pretty much gave yourself the answer here already from the first suggestion. After the Anglo-Soviet "Occupation" of Iran in August 1941, a fair bit of their correspondence travelled through this corridor until pretty much the end of the war. Known as the "Persian Corridor", for the later half of 1941 US-UK communications to Stalin and the Kremlin were channeled through the embassies in Tehran and from there by telegram signals onwards to their final destinations.^(1) Perhaps even more startling however, is just how important Iran was a channel of trade and aid rather than a communications hub for the Allies. Of the 17.5 million tonnes of Lend-Lease the US sent to the USSR, more than 7.9 million tonnes were sent through Persia (almost 45% of the total tonnage sent in aid).^(2) There's a good reason Tehran was the site of the first "Big-Three" meeting two years later in 1943: it represented the middle-ground for the three leaders. It was relatively close to the USSR so Stalin could monitor the progress (or lack thereof) of any Red Army engagements, Churchill was able to use the British Middle East Command's bases as travel points to the conference, and Roosevelt was practically the only reluctant one (Stalin had turned down his previous offers of Cairo, Basra, and Baghdad, all to ensure he did not have to fly to the conference).^(3)
The North Sea: It was less common for any correspondence between Washington, London, and Moscow to make its way East or West via the arctic convoys which braved the freezing cold, wolf packs and Luftwaffe Condors to reach the USSR. This is due to the simple fact that the convoys were not exactly guaranteed to make it to port, and the long journey times (even without attacks by Kriegsmarine or Luftwaffe forces) made it impractical for any wartime correspondence. What the arctic convoys did enable, as is rather obvious, was another flow of goods from Britain (and even as far as America) to the Red Army. Everything from planes, tanks, jeeps, boots, ammunition, and even food was shipped by these convoys. Though the Soviets in later Cold War fashion downplayed their significance, historians often consider that these convoys not only strengthened Allied unity and resolve, but may have helped lighten a massive burden off the Soviet shoulders during the war. Here's Russian historian Boris Sokolov on the matter:
On the whole the following conclusion can be drawn: that without these Western shipments under Lend-Lease the Soviet Union not only would not have been able to win the Great Patriotic War, it would not have been able even to oppose the German invaders, since it could not itself produce sufficient quantities of arms and military equipment or adequate supplies of fuel and ammunition.^(4)
Vladivostok: Of the three possibilities you've proposed, this is the only one we can definitively say "no" to. In a single word, the reason being is: Japan. Or more specifically, the fact that Japan and the British Empire were not on the best of terms. Though Japan had yet to strike at the Empire's holdings in Hong Kong and Singapore before December and February respectively, it was still in a trade embargo and formal suspension of relations with London, meaning that any correspondence making its way to Moscow via Vladivostok was likely to complicate matters further between Tokyo and Westminster. Washington was also unable to utilise Vladivostok as a communication stepping-stone, simply because of the fact that it would also be at war with Japan come December 7th, 1941.
So there we have it then. In the Fall of 1941 as Operation Barbarossa tore its way towards Moscow, the Allies communicated chiefly through their new conduit in Iran, but also through diplomatic missions which made the dangerous voyage through the North Sea by Royal Navy vessel and down to the Kremlin by train. It is these missions I might direct you to investigate further yourself, as they provide a clear geopolitical image of London being the "middle-man" between Uncle Sam and Uncle Joe for the majority of the war. To that end, I have attached alongside the sources below some further reading on those diplomatic efforts (each successes and failures in their own right). I hope my answer has somewhat (or maybe fully) answered your question! Feel free to enquire further about anything mentioned here.
Sources
[1] Ward, Steven R. Immortal : A Military History of Iran and Its Armed Forces (Georgetown University Press) 2009, pg. 176
[2] Coakley, Robert W. (2000) [1960]. "Chapter 9: The Persian Corridor as a Route for Aid to the USSR". In Greenfield, Kent Roberts (ed.). Command Decisions*. (*Washington: United States Army Center of Military History).
[3] Service, Robert. Stalin. (Harvard: Belknap Press of Harvard University Press). 2005
[4] Weeks, Albert L. "Russia's Life-Saver: Lend-Lease Aid to the U.S.S.R. in World War II, (Lanham, Maryland: Lexington Books). 2004.
Further Reading: