What is the difference between class_eval, class_exec, module_eval and module_exec?

I’m going to answer a bit more than your question by including instance_{eval|exec} in your question.

All variations of {instance|module|class}_{eval|exec} change the current context, i.e. the value for self:

class Array
  p self                     # prints "Array"
  43.instance_eval{ p self } # prints "43"
end

Now for the differences. The eval versions accepts a string or a block, while the exec versions only accept a block but allow you to pass parameters to it:

def example(&block)
  42.instance_exec("Hello", &block)
end
example{|mess| p mess, self } # Prints "Hello" then "42"

The eval version does not allow to pass parameters. It provides self as the first parameter, although I can’t think of a use for this.

Finally, module_{eval|exec} is the same as the corresponding class_{eval|exec}, but they are slightly different from instance_{eval|exec} as they change what is the current opened class (i.e. what will be affected by def) in different ways:

String.instance_eval{ def foo; end }
Integer.class_eval  { def bar; end }

String.method_defined?(:foo)            # => false
String.singleton_methods.include?(:foo) # => true
Integer.method_defined?(:bar)           # => true

So obj.instance_{eval|exec} opens the singleton class of obj, while mod.{class|module}_{eval|exec} opens mod itself.

Of course, instance_{eval|exec} are available on any Ruby object (including modules), while {class|module}_* are only available on Module (and thus Classes)