You're going to hate this one but let's just get it out there. Get a bigger washing machine and dryer. I know, I know. It's probably impractical. Most everyone's budget is insanely tight right now and if your washer is currently fine then it's out of the question. Once you are in the market, or you get your tax return, focus on washers that can hold a lot. It can cut the number of loads you need to wash per week in half. Now the realistic tips...
Use your start delay. People say to me all the time, "Of course, you're laundry is under control. You're home all day." Ugh, I don't spend all day doing laundry. I've got some short cuts. That's all. I technically start Sunday night and am done by lunch time on Monday. Typically, I toss in a load of colors Sunday night and put it in the dryer before I go to bed (usually after midnight). After, I start the dryer I get the whites ready to be started and set the 'delay' button for what ever gets me to 7 a.m.. In the morning, what's in the dryer gets put on my bed, the whites go in the dryer, and I start my second (and sometimes last) load of colors in the wash. So, yes, my washer is such that I usually wash 3 loads a week for my family of 6. Sometimes I wash a 4th load of sheets or permanent press. Even if you don't have a high capacity washer you can get 6 loads done in over the weekend and not lose much time. I'm talking just washed & dried...we'll get to folding later.
Wash clothes right side out. This might sound odd but it actually saves you some time when you go to fold because you're not wasting time turning the clothes right side out. It also gives you a nice chance to pre-treat any stains. So get the kids into that habit, tell your spouse, start fixing them as you toss them in the hampers.
When I asked myself what I hated most about doing laundry it was the whites. Four little boys + 2 adults = 84 socks. 84 SOCKS!!! Socks that look alike but they're a size off but the naked eye can't tell. You have to find it's mate in the pile of 84 socks and make sure it's the same size and then you have to pair it to the sizes of the others socks. See where I'm going? Socks are a total time suck. The same is true for the underwear although underwear isn't nearly the pain socks are. Getting everyone different brands is one solution but still you're going through a pile of socks dividing whose are whose.
My solution - wash everyone's white socks and underwear in their own lingerie bag. I have 4 large, zippered lingerie bags hanging on hooks in the laundry room. The boys put all their socks in there when they take them off. If your laundry room is far from the bedrooms hang the bags in the closet or on the outside of their hamper. The key is a large bag so the white aren't crammed in there and are free to move in the dryer and zippered so they don't open up. If they still feel a little damp after they go through the dryer just run them again with the next load.
You read in one of the paragraphs above I dump clothes from the dryer on to my bed. I then divide each family members clothes into their own laundry basket. I have one extra for miscellaneous things like dish towels, towels, and blankets. For me folding everything as it came out was a time suck. I was always folding AND I had piles of folded clothes everywhere because I'd divide it as I folded. I'd have 6 piles of shirts, 6 piles of pants, 6 piles of underwear, and it was just a matter of time before some kid ran through and scattered the piles. I found it easier to divide the clothes right out of the dryer into personal laundry baskets. This is where the white socks being in a lingerie bag is really helpful. Once all the loads were done I'd start folding and enjoy one of my prime time T.V. shows. OR you can do the next tip....
A lot of my friends have large families. Occasionally, someone will complain about all the laundry they have to fold. Then I think to myself, 'You've got 6 kids. That shouldn't be the case.' Have the kids fold their own laundry. My 9 year old folds his own, my 7 year old folds his own, and my 5 year old fold his own. I've found it to be a nice family time thing to do. I put on a movie for them to watch, give the kids their baskets of clean clothes, and they fold them and put them away. Then I'll make them popcorn for the rest of the movie.
Remember in Ghostbusters II when Peter told Dana in regards to laundry that there wasn't just clean and dirty. There were many subtle levels. It was funny but now that I'm a mom trying to cut down on the amount I wash that joke makes perfect sense. So wash just what needs to be washed. I'm the first to admit I'm a bit of a germaphobe. Any clothing that goes outside is pretty much branded, DIRTY. However, if the boys stay inside, eat neatly, and don't do much I give the clothes another day. Jeans might get a few days depending on what they did at school.
The dreaded laundry chore is mostly about finding your rhythm and some team work.