I know something about it, but had not heard of the quad mount, which I presume never saw service. My take on the Russian 37 mm AA (from my forthcoming book on automatic cannon and their ammunition):
37 mm M1939: 37 x 252SR ammunition (aka 37 x 250R or SR).
This gun and its ammunition were designed at short notice in 1938 when it was felt that the 45 mm M1939 was too large; this 37 mm gun, designated ZIK-37 or 61-K, is effectively a scaled-down version of the 45 mm and is therefore a slightly smaller version of the 40 mm Bofors M32. It was fed via 5-round vertical clips and fired at 160-170 rpm. A twin-barrelled version of the wheeled land mounting was also made as the 47-V, but this saw more export sales than Russian service; the SU-37 SPAAG also saw only limited service. Nearly 20,000 army guns were produced by the end of WW2, after which Russian production ceased.
The appearance of the M39, with the boxy receiver and vertical feed, is very close to that of the German naval 3,7 cm Flak C/36 and Flak M42. Presumably all of these weapons were based on the Bofors system but the exact development relationship is unclear. The 37 mm M39 was developed with remarkable speed; possibly the Russians already had detailed information about the Flak C/36, as Germany provided various weapons for the Russians to evaluate.
Naval versions of the gun were designated as follows: 70-K (single barrel, air-cooled) over 3,000 made between 1941 and 1956); 66-K (twin barrels, water-cooled) prototype only, cancelled in favour of; V-11 (twin-barrelled, water-cooled, stabilised mounting) and V-11M (improved sights) of which 1,300 were made from 1944 to the early 1980s.
These weapons were widely sold abroad, and were made in large numbers by China. They remain in service in various countries, in some cases with upgrades to the mounting and/or fire control system; most recently in Pakistan, with 700 delivered.