A class, in current, conventional OOP, is a collection of data (member variables) bound together with the functions/procedures that work on that data (member functions or methods). The class has no relationship to the other three terms aside from the fact that it “contains” (more properly “is associated with”) the latter.
The other three terms … well, it depends.
A function is a collection of computing statements. So is a procedure. In some very anal retentive languages, though, a function returns a value and a procedure doesn’t. In such languages procedures are generally used for their side effects (like I/O) while functions are used for calculations and tend to avoid side effects. (This is the usage I tend to favour. Yes, I am that anal retentive.)
Most languages are not that anal retentive, however, and as a result people will use the terms “function” and “procedure” interchangeably, preferring one to the other based on their background. (Modula-* programmers will tend to use “procedure” while C/C++/Java/whatever will tend to use “function”, for example.)
A method is just jargon for a function (or procedure) bound to a class. Indeed not all OOP languages use the term “method”. In a typical (but not universal!) implementation, methods have an implied first parameter (called things like
self or the like) for accessing the containing class. This is not, as I said, universal. Some languages make that first parameter explicit (and thus allow to be named anything you’d like) while in still others there’s no magic first parameter at all.
Edited to add this example:
The following untested and uncompiled C++-like code should show you what kind of things are involved.
void setMemberVariableProcedure(int v)
memberVariable = v;
void plainOldProcedure(int stuff)
cout << stuff;
int plainOldFunction(int stuff)
return 2 * stuff;
In this code
getMemberVariableFunction are both methods.