(speaking about the Holodomor exclusively here)

There were some attempts to provide international aid, though nothing led by Western governments themselves. A letter written by Laurence Collier of the British Foreign Office specifically states that the government had “a certain amount of information about famine conditions,” but “[did] not want to make it public, however, because the Soviet government would resent it and our relations with them would be prejudiced.” The American government at the beginning of the famine did not yet have formal diplomatic relations with the Soviet Union, and were likewise being very careful.

The reactions of everyday people were influenced by the fact that the stories coming out of Russia were often contradictory. Some reporters, like Walter Duranty, denied that a famine was even taking place. The news was alarming enough, however, that many people in the U.S. (especially Ukrainian immigrants) tried to appeal to the government to supply aid. In Austria, Theodor Cardinal Innitzer set up an International Relief Committee, working with Dr. Ewald Ammende. J. H. Rushbrooke of the British Free Church Council is described in contemporary accounts as taking a “leading role in international relief activities after the 1933 famine,” as well. A note from the British Foreign Office shows that Rushbrooke was involved in a “Torgsin parcels scheme," a type of relief effort supported by the United British Appeal organization.

Torgsins were “trade with foreigners” stores that existed from 1931-1936. They accepted foreign currency or valuables in exchange for bread and other goods, and provided a way in which the Ukrainian diaspora could assist their family members back home. This method was utilized by Ukrainians of Mennonite and Jewish descent in particular. While the Soviet government rejected other forms of international aid, they welcomed hard currency as a resource to drive industrialization.

If you’re interested, there was a commission formed to investigate the Ukrainian famine in 1985… the full text is available online and contains some testimony from people who lived through it: http://babel.hathitrust.org/cgi/pt?id=mdp.39015014630530;view=1up;seq=7