Almost everyone in the family can help with the laundry in some way. Teach your children when they're small how to sort whites and colors. A different hamper for each color will save time. For those kids who find laundry a real chore, putting a basketball hoop over the laundry basket might change their minds.
Do laundry every day and fold it right away. Letting laundry build up makes the task daunting. Plus, you can save ironing time. If you have the space and can afford it, buying two washers and dryers could be a good investment.
Make sure that each child in the family has a space for their clean, folded clothes and knows it's his responsibility to put those clothes away. For fast sorting of clothes, mark the tags of each child's shirts and pants with a different color marker.
Color-coding is important for socks too, especially when they all look alike. Sew a different color thread in the toes for each child or mark with a colored permanent marker.