At the risk of being too simple, even simplistic, we can see the differences among the approaches as lying along two dimensions.
The first and second methods see legal meaning as more or less independent of general social meaning, while the third and fourth emphasize instead the degree to which law as well as legal language is immersed in social practices.
On a different dimension, the first and third methods emphasize the meanings of particular words, while the second and fourth tend more to look at the significance of the rule as a whole.
If we array the methods along these dimensions, we get the following:
(1) Formal definitions and common sense meanings.
(2) Emphasis on purpose of rule and paradigmatic or stereotypical examples
In the course of ordinary LEGAL ANALYSIS and JUDICIAL REVIEW, all four methods are commonly used.
For someone to become adept at legal argument, all four must be learned.
There are also arguments for and against using one method or another as well as arguments for when and under what circumstances it is best to use one method or another, but that, that's for later, later on.
AND . . . If we shift our attention from what advocates can do, to what judges have done, to JUDICIAL REVIEW, we find all four methods used by the students in their discussion of whom should be fined $50 for leaving trash on the beach in the OPINIONS OF JUDGES IN SUPREME COURT CASES and in THE CASES that students will be presenting in class the course of the spring semester in PHILOSOPHY 117.