Is it possible to create an empty multidimensional array in javascript/jquery?

Maybe something like that in your each:

if ( imageArray[item.tags] != null ){
   imageArray[item.tags][imageArray[item.tags].length] = item.url_sq;
}else{
   imageArray[item.tags] = [];
}

JavaScript doesn't have true multidimensional arrays (heck, it doesn't even have true regular arrays...), but, like most languages, it instead uses arrays of arrays. However, to me it looks like you need an object (kinda similar to PHP's arrays) containing arrays.

var data = {
    tag1: ['URL_1', 'URL_2', 'URL_3', 'URL_n']
};
// Then accessed like:
data.tag1; // ['URL_1', ...]
data.tag1[0]; // 'URL_1'
data.tag1[1]; // 'URL_2'
// etc.

So, you're problem would look something like this:

var tags = {};
$.each(data.photoset.photo, function (i, item) {
    $.each(item.tags.split(" "), function (i, tag) {
        if (!tags[tag])
            tags[tag] = [];
        tags[tag].push(item.url_sq);
    });
});
// tags is now something like:
// {
    "foo": ["/url.html", "/other-url/", ...],
    "bar": ["/yes-im-a-lisp-programmer-and-thats-why-i-hypenate-things-that-others-might-underscore-or-camelcase/", ...],
    ...
//}

var arr = [];
arr[0] = [];
arr[0][0] = [];
arr[0][0][0] = "3 dimentional array"

Multi dimentional arrays have a lot of gaps unless they are used properly. A two dimensional array is called a matrix.

I believe your data contains a space seperate string called "tags" containing the tags and a single url.

var tagObject = {};
data.photoset.photo.forEach(function(val) {
  val.tags.split(" ").forEach(function(tag) {
    if (!tagObject[tag]) {
      tagObject[tag] = [];
    }
    tagObject[tag].push(val.url_sq);
  });
});
console.log(tagObject); 
/*
  {
    "sea": ["url1", "url2", ...],
    "things": ["url4", ...],
    ...
  }
*/

I don't know how it returns multiple tags.

I think the syntax you are attempting to achieve is something like the following:

var item = {"tags":"blah","url_sq":"example.com"}; // for sake of example.
var imageArray = [];
$.each(data.photoset.photo, function(i, item) {
   imageArray.push({"tags":item.tags,"url":item.url_sq});
});

and then reference it like this:

imageArray[0].tags
imageArray[0].url
imageArray[1].tags
imageArray[1].url
...