Dashboard – get status and position of metaboxes and pass them to ajax method

You can hook into the sortstop event of the sortable metaboxes, and read the current state:

jQuery( function( $ ) {
    $( '.meta-box-sortables' ).bind( 'sortstop', function( event, ui ) {
        var sortData = {};
        $('.meta-box-sortables').each( function() {
            sortData[this.id.split('-')[0]] = $(this).sortable( 'toArray' );
        } );
        console.log( sortData );
    } );
} );

You can also hook into the events that hide or reveal metaboxes, but this requires some more work on your side, since WordPress does not provide nice events for this. See the postbox.js script for more details.

There are other answers on this site that deal with the Ajax part.