You can get the concatenated year and week number (200945) using the YEARWEEK() function. If I understand your goal correctly, that should enable you to group your multi-year data.
If you need the actual timestamp for the start of the week, it's less nice:
DATE_SUB( field, INTERVAL DAYOFWEEK( field ) - 1 DAY )
For monthly ordering, you might consider the LAST_DAY() function - sort would be by last day of the month, but that should be equivalent to sorting by first day of the month ... shouldn't it?