Nested JSON objects - do I have to use arrays for everything?

You don't need to use arrays.

JSON values can be arrays, objects, or primitives (numbers or strings).

You can write JSON like this:

{ 
    "stuff": {
        "onetype": [
            {"id":1,"name":"John Doe"},
            {"id":2,"name":"Don Joeh"}
        ],
        "othertype": {"id":2,"company":"ACME"}
    }, 
    "otherstuff": {
        "thing": [[1,42],[2,2]]
     }
}

You can use it like this:

obj.stuff.onetype[0].id
obj.stuff.othertype.id
obj.otherstuff.thing[0][1]  //thing is a nested array or a 2-by-2 matrix.
                            //I'm not sure whether you intended to do that.

You have too many redundant nested arrays inside your jSON data, but it is possible to retrieve the information. Though like others have said you might want to clean it up.

use each() wrap within another each() until the last array.

for result.data[0].stuff[0].onetype[0] in jQuery you could do the following:

$.each(data.result.data, function(index0, v) {
    $.each(v, function (index1, w) {
        $.each(w, function (index2, x) {
            alert(x.id);
        });
    });

});

Every object has to be named inside the parent object:

{ "data": {
    "stuff": {
        "onetype": [
            { "id": 1, "name": "" },
            { "id": 2, "name": "" }
        ],
        "othertype": [
            { "id": 2, "xyz": [-2, 0, 2], "n": "Crab Nebula", "t": 0, "c": 0, "d": 5 }
        ]
    },
    "otherstuff": {
        "thing":
            [[1, 42], [2, 2]]
    }
  }
}

So you cant declare an object like this:

var obj = {property1, property2};

It has to be

var obj = {property1: 'value', property2: 'value'};