Order by day_of_week in MySQL

Why not this?

ORDER BY (
    CASE DAYOFWEEK(dateField)
    WHEN 1 THEN 7 ELSE DAYOFWEEK(dateField)
    END
)

I believe this orders Monday to Sunday...

Either redesign the column as suggested by Williham Totland, or do some string parsing to get a date representation.

If the column only contains the day of week, then you could do this:

ORDER BY FIELD(<fieldname>, 'MONDAY', 'TUESDAY', 'WEDNESDAY', 'THURSDAY', 'FRIDAY', 'SATURDAY', 'SUNDAY');