The disjunctive case is a grammatical case in French, where (like other cases) it has a distinct form only for pronouns.
Moi et lui, nous sommes allés au parc. I and he, we went to the park.
Nous, nous sommes pour; eux, ils sont contre. We are for; they are against.
It also serves as a sort of prepositional case, in the sense that pronouns marked by preposition take the disjunctive (i.e., avec lui, pour toi, etc).
For non-3rd person verbs in the imperative mood, the disjunctive pronouns are used to mark the direct and indirect objects of a transitive verb, as in the accusative case. So we have écoute-moi (listen to me), dis-moi (tell me). However, in the third person (both singular and plural), the disjunctive is not used. This is likely because French preserves the dative/accusative distinction in the third person, and so use of the disjunctive would result in a loss of information. For example, you say tue-le (kill him), but dis-lui (tell him) -- examples of the accusative and dative, respectively. Note that in this case "lui" is the dative third person singular pronoun, not the disjunctive -- the difference may be seen in the 3rd person feminine, where the disjunctive is "elle" but the dative is still "lui". See also French grammar.
The vocative case is the case used for a noun identifying the person being addressed, found in Latin among other languages.
In Latin, e.g., the nominative case is lupus and the vocative case is lupe!
In English the vocative case is not marked, but English syntax performs a similar function; witness: "John, could you come here?" or "I don't think so, John", where "John" is neither subject nor object of the verb, but rather indicates the person to whom the statement is being addressed.