Search Index of the array from the json value using indexOf

Your logic fails because objects are unique, unless they refer to each other.

Notice these examples:

var a = {};
var b = {};
console.log(a == b); // false

var a = {};
var b = a;
console.log(a == b); // true

So when you use indexOf it will search the array for a == element and will always give false.

You could make an approximation, but that is not reliable like this:

var u = usuarios.map(JSON.stringify);
console.log(u.indexOf('{"nome":"José","id":3}')); // dá 2

But in this case you compare strings and lose the advantage of using objects. As you suggested the best is with cycle for and with break or return so you do not need to reach the end, but even there you have to compare values and not the object itself (except as stated above that you have a reference in a variable):

function getId(nome) {
    for (var i = 0; i < usuarios.length; i++) {
        if (usuarios[i].nome == nome) return i;
    }
}

console.log(getId('José')); // dá 2

jsFiddle: link