I would make a stored procedure for each operation mainly for maintainability. Each store procedure will be coherent to its task. If you have all the actions in one stored procedure then its going to contain conditions which will bulk up the lines of code and could increase the number of variables that really could make it difficult to fix errors.
Also the parameters, you could have to supply the parameters for all the actions regardless of whether the given action actually needed them or not. ie. delete action would only require the identifier, but you have to supply other parameters because they are required for insert and update actions