I'm primarily asking about from the end of the Russian Revolution to before the start of World War Two.
With regards to Italy, the matter is very complicated.
The Italian Communist party had a love-hate relationship with the USSR.
The Italian Socialist Party was a generally capitalist-oriented, pro-European, "Third Way" party, although when he was Prime Minister, Socialist leader Bettino Craxi enjoyed a cordial working relationship with Ronald Regan.
And lastly, the Italian Social Democrats never got enough votes for anyone to ask them for their opinion, but they entered in a number of coalitions with the pro-American Christian Democracy party.
Il Partito Comunista Italiano (Electoral Range: fluctuating between 22% and 30%)
The Italian Communist Party (PCI) was the spiritual successor to the Communist militias which had taken up arms against the Fascist Regime between 1944 and 1945. Although these militias were composed of existing anti-fascist activists as well as returning soldiers/deserters, they received small albeit perceptible amounts of aid from the Soviet Union. The "Sovietization" of these militias, and by extension the "sovietization" of opposition to the dying regime, definitely was tangible. Although he's not a historian, in Hemingway recalls the mood of the moment in Across the River and Into the Trees by recounting that the owner of Harry's Bar in Venice has bought an equal number of cases of Whiskey and Vodka, being unsure of who would liberate Venice first.
In its early days, the most members of the Italian Communist Party leadership were definitely pro-USSR, and the General Secretary Togliatti had a direct line to Moscow. However, by the 1950s it became increasingly difficult for the PCI to justify increasingly evident oppression in the Eastern Block, culminating in the Hungarian Revolution of 1958. Togliatti began advertising "The Italian Way Towards Socialism" in the 1958 election, signaling that the pro-USSR faction within the party was definitely in the minority. By the 1968 Prague Spring, the PCI was actively condemning the Soviet Union. By 1976, the General Secretary of the PCI, Enrico Berlinguer, declared in a high-profile interview in the Corriere della Sera newspaper that his “Eurocommunism” was unconditioned by the regimes behind the Iron Curtain, and that at any rate he felt safer living under the umbrella of NATO than he would be in a Warsaw Pact country. A vaguely pro-American declaration, although Berlinguer wasn't by any means supportive of US policies in Europe and the world.
In spite of Berlinguer's official line, there remained a backbone of pro-USSR administrators in the Italian Communist Party such that when Berlinguer suffered a fatal stroke at a rally in 1984, the Communist Party leadership sought refuge in pro-Soviet nostalgia, only to lose any ability to form coherent policy after Michail Gorbachev’s reforms within the Soviet Union gained steam.
Il Partito Socialista Italiano (electoral range: between 7% and 15%)
The Socialists were in great part perceived as "Diet Leftists," seeing as the Italian Communist Party itself was founded as a direct reaction to the 1921 PSI congress when Socialist Party leaders denounced the use of arms. In fact, the Italian Socialist Party (PSI) was only ever the "Younger Brother" of the Italian Communist Party until the 1960's, when youth activism revealed the ruling Christian Democrats (DC) were very unpopular with younger voters, pushing together center-left coalitions. Prior to then, there had been a "Unity of Action" between the Communist Party and the Socialist party, and this had extended to foreign policy: the Socialists opposed Italian entry into NATO in 1949, but also began to denounce the Soviet Union in the 1950s.
However, unlike the Communists, in the Socialist party the pro-Soviet faction was only small (albeit vocal) and rapidly evaporated. By the time the Socialist-led governing coalition of the 1980s came to power, the Socialist Party was committed to a strong pro-European line. Relations with the USSR were non-existent, while relations with the US were pragmatic: most prominently, Craxi affirmed Italian sovereignty during the hijacking of the Italian cruise ship “Achille Lauro” off the coast of Egypt by members of the Palestinian Liberation Front. Already peeving Italy’s NATO allies by negotiating with the terrorists, after the hijackers’ getaway plane was coerced by American fighter jets to land on a NATO base in Sicily, Italian Carabinieri (the national Gendarmerie) impeded a detachment of American Special Forces operatives to apprehend the four hijackers, so that they could be tried in Italy. In spite of not realizing that one of the negotiation aids sent by the Palestinian Authority had been intimately involved with the hijacking, Craxi’s firm stance during the crisis strengthened his public image.
Partito Socialista Democratico Italiano (electoral range: between 2.5% and 6%)
The Italian Social Democrats had originally been founded as a splinter group of the Socialist Party in 1947. The Socialists had proven to be too centrist for some important members of the party. However, their focus on social welfare policy quickly led them to be perceived as a single-issue centrist party, seeing as the ruling Christian Democrats were also not opposed to generous welfare policies. Their impact on Italian foreign policy was negligible, although they did act as important scale-tippers in numerous governing coalitions.
Sources on European Political History you might be interested in:
The Italian Revolution: The End of Politics, Italian Style? (1995)
and
European Integration: A Concise History. (2012)
Both by M. Gilbert