A class-action lawsuit is a lawsuit seeking monetary award for damages done to a large number of people. Frequent class-action lawsuits occur against corporations for some product defectiveness or defective drug problem.
A class action lawsuit typically does not get the individual plaintiffs much money in awards, but class action suits are effective in changing a company's practices or getting faulty products out of the market. Personal injury lawsuits can use the class-action status if many people were injured in the same way.
A civil suit is any lawsuit filed against someone else (or some entity) seeking monetary compensation. Personal injury lawsuits are a type of civil suit, though so are many other kinds of lawsuits depending on the type of redress sought or type of crime committed.
Criminal lawsuits are a kind of suit filed by the government against individuals or entities (such as companies) seeking social redress. Criminal lawsuits seek some form of punishment not limited to monetary fine, including incarceration, probation, or other forms of law enforcement action.