My boys are 6 and 12, and my 12 year old is insanely organized, so I'll focus on my 6 year old (C) for this response. My husband and I are very neat and organized, too, so my poor youngest is a fish out of water in our house. We have to constantly guide him toward organization.
It helps to have an easy way to put toys away. We have a toybox in C's room, and two large drawers in the coffee table in the living room that are also for toys. In addition to that, other toys are in bins that can be taken out of his closet when he is playing with them. There is a bookcase in the living room that has C's books on the bottom two shelves. He knows he is responsible for putting away everything he takes out. I also remind him not to take out too much at once. As I walk through the room, I'll remind him to clean up one mess before he starts another. He's pretty good at keeping things under control.
His biggest issue is with his desk. He loves drawing, cutting, gluing, etc., and his desk becomes a disaster area quickly. Now we have a rule that once a week he has to clean up his desk. Lately, I haven't even had to remind him. He knows that if it starts to look crazy, he needs to clean it up.
All messes have to be cleaned up before we leave the house, and before bed. No exceptions. I don't clean up any toys anymore, and haven't for a couple years; I just remind when it's time to start putting things away.
I hope you find a system that works for your family. It is so much nicer when things run smoothly so that you do have time to enjoy each other. :)
Oh, as for housework, I'm a teacher, and my husband is a manager in car sales so he works a ton. He does get one day off during the week, and he cleans the entire house that day (I love that man!). Then I do the laundry and touch up any cleaning that needs to be done. Both kids help with the cleaning, and with caring for the pets. Mostly they keep their rooms neat and put their clothes away. Our older son helps care for his younger brother sometimes, too. On Sunday, my husband's other day off, we can relax and play together instead of doing chores.
Homework is done while I cook dinner so that I can help if needed. Projects are also done during this time, or on Saturdays. Our 6 year old does his 15 minutes of reading aloud in the car while I'm driving to pick up our 12 year old from school. It's his choice. I thought he'd want a break after school, but he wants to get it done.
Sorry this is long. I hope it helps.