How old are your children? can you teach them how to wash, fold & put away? I remember having great fun matching socks with grandma when I was pre-school aged.
As for us, we do laundry 1x a week. My husband does 3-4 double loads on thursday or friday evening when the laundry room is not busy. We then dump all the laundry on the living room floor and put it away the following morning. A half hour each for the wash and dry, and a half hour for the folding.
things to make your job easier- 1. buy only one type of sock/ underpant per person. Hubby has 1doz pairs of black gold toe socks. I have 1 doz pairs of knee high argyles. No need to fuss over matching.
2. have 4 sets of clothes per kid. one for school, one for indoor play, one for outdoor play and pajamas. the school, indoor play and pajamas can go for more than one wear, unless they are stained. they are kids afterall. no one is going to fret if they wear the same khakis two or three days in a row.
here's an idea. give each kid a "cubby" it could be a box or a hanging coatrack in the foyer, or mudroom. They strip down and wash as soon as they are in from play. They change into their indoor clothes. You can swap out clothes if you think they are too dirty for wear.
3. why are you organizing dirty laundry? buy a color safe bleach and put it all through a cold wash.
4. laundry is a fact in everyone's life, but yours seems to have gotten out of control. Consider what you could be doing if you got the laundry in check. Give yourself a treat as an incentive.
5. get it out of the kitchen. you are making it harder for yourself by having to shift it around a bunch.