Both liberalism and conservatism, in the context of American and West European politics and government, advocate democracy. Where the two diverge is in the question of income inequality. Liberals tend to favor the redistribution of wealth to ensure a greater level of income parity -- a policy executed through a graduated tax system that taxes those on the higher end of the economic spectrum far higher than those further down the socioeconomic ladder. Conservatives, in contrast, tend to support a greater level of economic freedom, albeit one that results in higher levels of income disparity, as free enterprise with minimal governmental intrusion or regulation is the economic model of choice. Nationalism does not necessarily have anything to do with the three topics posed in the question (democracy, economic equality, and joint ownership), as it exists in virtually all political and economic systems and is a product of a common sense of national identity and pride in one's country. The trickier question involves socialism. Socialism can exist in both democratic and autocratic political systems, although it definitely leans towards the latter, as the major means of production (e.g., large, economically-vital industries like energy and steel) are state-owned and economic freedom is minimal. Under both liberal and socialist systems, joint ownership is more prevalent, as liberals and leftists are more supportive of government control of the economy. Socialism ostensibly equates to economic equality, but, in practice, economic disparities are more striking in socialist systems than in democratic ones, as the experiences of the former Soviet-controlled East European economies demonstrated. In such systems, the middle class is all-but-nonexistent, as political party and government apparatchiks enjoy a far higher standard of living than the rest of society.
All four categories can be compatible with democracy to greater or lesser extents, but socialism, as noted, involves far less economic freedom (i.e., far less opportunity for private enterprise to grow and prosper) than liberals and conservatives advocate. Only in the most extreme form of nationalism, such as the system of National Socialism imposed by Germany's Nazis during the 1930s, does economic freedom necessarily suffer, as the government imposes stringent controls on economic activities and sets industrial policies that dictate what gets produced and in what quantity -- a characteristic common also among communist systems, such as in the former Soviet Union, Venezuela since the rise of the late Hugo Chavez, and Cuba under the Castro brothers.