Or more than three sides, even. Reading over the topic it seems that there were a number of different factions involved - the Wehrmacht, the Chetniks, Ustase, the Communists.... and not only all with different aims, but often directly contrary ones, so there seems to have been a lot of fighting between all of them. Was the situation more one that saw brief alliances of convenience to focus on a common enemy, or more one that truly saw multiple factions all engaging each other?
Assuming that there were said temporary alliances, how did ethnic tensions dictate those arrangements? Were there groups more willing to cooperate for a time, and others who always would say "hell no"? Also given those ethnic tensions, what sort of involvement in the Holocaust and other ethnic cleansing carried out by Nazi Germany do we see from groups who were opposed to occupation, but not particularly against the killings being carried out by Germany?
Part 1:
To start out on the more unprofessional side: My Southeastern Europe professor used to say, the Second World War in the Balkans (up to and including Greece) are the inception of wars: It's ethnic conflict within political conflicts within civil wars within a war of national liberation within a world war. That might sound flippant (and you might right now make this face) but unfortunately for the people forced to live through it, it fits the situation.
Ok, to start at the approximate top:
The Kingdom of Yugoslavia before the Second World War was a state rive with difficulty. Ever since its inception (heh) at the end of World War I, one of or rather the major internal conflict revolved around how the state did or rather should reflect the nationalities in it. Mainly, it was about Serbia taking a rather dominant role while especially the political establishment of the Croatian part of the state felt that there should be stronger representation of Croatia and Croatian interests on the state (Slovenia subscribed to this too but they did and always had a bit of a special role, even in post WWII socialist Yugoslavia). This went as far as blocking parliamentary proceedings within the kingdom of Yugoslavia and the establishment of the dictatorship of King Alexander I in 1929. This was the same king later killed by the Ustasa and the radical Macedonian Revolutionary Organization in 1934 which lead to further tensions along ethnic and political lines within Yugoslavia.
I'm mentioning this because it is important to know at least a bit of the back story for better understanding of the consequences of Nazi occupation. As foreign occupations are known to do, they in some cases tend to carry over internal conflicts in the occupied countries into armed struggle given the right circumstances. Such was the case Yugoslavia. The specific occupational policy in Yugoslavia needs to be understood in terms of German improvisation. The German attack on Yugoslavia and Greece and their occupation was not in as much planned as it was a military and political inconvenience for German leadership. Having planned the attack on the Soviet Union in 1941, Germany felt the need to militarily intervene in the Balkans because of the disastrous Italian invasion of Greece the same year and the officers' coup d'etat in Yugoslavia. Having long planned to militarily secure the southern flank of its attack on the USSR and to keep hold on the economic resources of Yugoslavia, Nazi Germany pressured it into the Axis. However, this was frowned upon by several political factions, especially in the Yugoslavian military, which was dominated by Serbs. And so, in March 1941, several high ranking officers initiated a coup d'etat with their new government announcing that it was not intending to honor the Axis agreement with Germany. This lead to the German invasion of April 41.
After a quick military victory over the Kingdom of Yugoslavia, the Third Reich faced the dilemma of how to organize occupation in a manner that was to spare them using much needed military resources. This lead to the creation of the Independent State of Croatia (NDH) under the Ustasa, which itself was more of an improvised solution since the most Croatian party with the most support refused collaboration with the Nazis and the Ustasa was by far not a party supported by the masses but rather a conspiratorial revolutionary organization.
So while Croatia became a satellite state with a rather dubious collaborationist regime, Bosnia was incorporated into Croatia, Slovenia annexed by the Third Reich, and what was called "rump Serbia" placed under the administration of the Wehrmacht (the latter due to Hitler's hatred of the Serbs, him being an Austrian).
To make things even more complicated, large swaths of territory of former Yugoslavia was placed under Italian occupation seeing as to how Mussolini claimed the Mediterranean as his domain.
With the occupation, the attack on the Soviet Union lead the Communists to spring into action. The Communists in Yugoslavia had long experience with covert struggle given they were outlawed under the dictatorship and many of their cadres were Moscow trained and experienced from the Spanish Civil War.
At the same time, resistance was initiated by many of the former Serb army officers in form of the Chetniks. Contrary to the Communists who styled themselves as the People's Liberation movement, the Chetniks, formally under the leadership of Draza Mihalovic, fought nominally for a vision of Greater Serbia to be build after liberation, thus making them almost exclusively appealing to people who thought of themselves as Serbs.
So, in 1941 you have the Germans and the Italians occupying the country, the Ustasa initiating a campaign of ethnic cleansing against the Serbs and Roma in their territory, the communist Partisans fighting for socialist revolution, the Cetniks nominally fighting for Greater Serbia but really just being a amalgamation of different, mostly monarchist Serbian army officers, and - to make matters even more complicated - organized bands of Muslims fighting against virtually everybody in their territory and from September 1941 the Serbian puppet government under General Nedic. Three-sided doesn't even begin to cover it.
As to answer your first question: There were brief alliances of convenience such as in 1941 when communist Partisans and Cetniks in Serbia effectively teamed up against the Germans. From June to December the country was engulfed in what is known as the Serbian national uprising. The alliance was incredibly effective against the stretched out and poorly trained German troops in the country, forcing them to retreat to the major urban centers and effectively establishing the first liberated territory in Europe, the Uzice Republic. This uprising was brutally put down by the German occupational forces once they were reinforced and instituted a policy of hostage reprisal quotes. Here, we also see the first cracks in the alliance between Cetniks and Partisans since the Cetniks couldn't retreat like the Partisans since they were stronger based locally.
Another case of shifting alliances are the armed bands of Muslims in Bosnia defending their homeland basically against everybody at first. Muslims were treated by the Ustasa at first as "Croatians of Muslim faith" and heavily attacked by the Cetniks. Later that alignment shifted against the Ustasa and so several political leaders of Bosnian Muslims collaborated with the Germans who were seen as the better choice in defending Muslim interests despite the Germans at the time collaborating with the Cetniks (or at least major parts of the faction) against the Partisans.
Also, on occasions, there were what in essence amounts to armistices between Partisans and Italians, especially when the Italians allowed the Partisans to pass through their territory in exchange for the assurance that they would not fight them. In short, many alliances were constantly shifting and often not kept by all parts of one side (especially with the more homogenous ones of Muslims, Cetniks, and to a degree the Ustasa).
Part 2:
As for groups more willing to cooperate, these were influenced by ethnic considerations and political ideology. You have the greater part of the Cetnik movement collaborating with the Nazis against the Communists despite Nazi support for the Ustasa and German hatred of Serbs. You have Muslims willing to collaborate with the Germans against Cetniks, Ustasa, and Communists because of religious, ethnic, and political considerations. You have Partisans making agreements at times with the Italians because of practical considerations. What I am describing here can not even begin to extensively cover all the intricacies of the war in Yugoslavia.
As for the last question concerning the Holocaust and ethnical cleansing:
The ethnic cleansing against Serbs initiated by the Ustasa was actually something several German occupation officials objected to. The Ustasa ran the third largest concentration camp in Europe (after Auschwitz and Majdanek) in Jasenovac and they killed thousands of Serbs. The German authorities saw this as a factor of instability in the region and therefore tried to rein in their ally.
At the same time, several armed bands of Muslims and Cetniks helped German forces to basically murder whole villages of Croats and Serbs suspected of supporting the Partisans while at the same time, the Cetniks killed scores of Muslims with a German placet and vice versa for Muslims and Serbs. As for killing of the Jews, there simply was not the chance to participate since the Serbia Jews were all killed by the beginning of 1942.
As you can see I am trying hard to cover this extensively but given how difficulty and affected by shifts the situation is, I would be happy to answer any more specific follow up questions and heartily recommend you check out the sources I will list below.
In short, the groups most willing to collaborate with the occupying forces were parts of the Cetniks and certain organized Muslims while the Partisans did make temporary arrangements but as a general rule did not collaborate.
Sources:
Misha Glenny: The Balkans: Nationalism, War and the Great Powers, 1804–1999.
Mark Mazower: Hitler's Empire: Nazi Rule in Occupied Europe (Allen Lane, 2008).
Mark Mazower: The Balkans: From the End of Byzantium to the Present Day (Phoenix, 2002).
Mark Mazower: Dark Continent: Europe's 20th Century (Knopf, 1998).
Ben H. Shepherd: Terror in the Balkans. German Armies and Partisan Warfare (Harvard 2012).
Klaus Schmider: Partisanenkrieg in Jugoslawien 1941-1944. Munich 2000.
Holm Sundhaussen: Geschichte Jugoslawiens 1918–1980. Stuttgart 1982.
Holm Sundhaussen: Jugoslawien und seine Nachfolgestaaten 1943–2011. Eine ungewöhnliche Geschichte des Gewöhnlichen. Böhlau, Wien 2012.
Walter Maoschek: Serbien ist judenfrei, Oldenburg 1994.
Alexander Korb: Mass Violence Against Gypsies in Croatia, 1941/42,’ in Anton Weiss-Wendt (ed.) The Nazi Genocide of the Roma: Reevaluation and Commemoration, ed.
Alexander Korb: ‘Understanding Ustaša Violence’, in Journal of Genocide Research, 12 (2010), 1–18.
Milovan Djilas' memoires about the Partisan war.
Borković, Milan. Kontrarevolucija u Srbiji – Kvislinška uprava 1941–1944.
Timofejev, Alexej J (2011). Rusija i Drugi svetski rat u Jugoslaviji.
Tomasevich, Jozo (2001). War and Revolution in Yugoslavia: 1941–1945. Stanford University Press.
