This question can be answered with books upon books of literature. I will try my best to distinguish the three through operational definitions- how they function. Common law is the accepted practice of law throughout the United States. Common law is the practice of law where the government is the initiator of proceedings against a defendant (http://www.lectlaw.com/def/c070.htm). In common law situations, accepted legal practices are substantiated through decisions and laws that have been codified and ruled upon by judges within the bounds of the legal system. There is a legal punishment rendered if the defendant is found guilty with a judgment of a legal fine paid, incarceration, or execution. There is a burden of proof that the prosecution must meet in a common or criminal law case that ensures that the guilt of the defendant must be proven beyond a reasonable doubt. Justice is defined as "guilty" or "not guilty." In civil law cases, the government, in the form of a judge, is asked to settle disputes between two parties, where one has initiated a lawsuit against another (http://www.rbs2.com/cc.htm#anchor333333). The parties are usually compensated monetarily in a civil law case. There is no government prosecution of a defendant in a civil case. Civil cases have a lesser burden of proof and the issue of monetary compensation is invoked to ensure that the term of "guilt" is not so clearly defined, but is addressed through money. Socialist law is the official name of the legal system used in Communist nations:
"It is based on the civil law system, with modifications and additions from Marxist- Lennist ideology. The most important of these modifications is providing for most property to be owned by the state or by agricultural co-operatives, and having special courts and laws for state enterprises" (http://www.economicexpert.com/a/Socialist:law.html)
A primary difference in Socialist Law is that the government assumes the responsibility of almost combining civil and criminal courts, especially in the compensation of property, which goes to the state.