I'm working on this myself. I used to have a clean house every day and I would load the dishwasher and tidy the children's rooms every evening while DH bathed them and read them stories, so even their rooms stayed clean. When they had afternoon naps, I would tidy the rest of the house, clean up any toys they had been playing with, clean the kitchen, bathrooms, do laundry, whatever, until they woke up. On the weekends, DH and I would share the big jobs, dusting, vacuuming, mopping, yard work, finishing the laundry, changing sheets, scrubbing the bathroom(s) and we'd be done, free to enjoy the rest of the weekend after a couple of hours of work.
Now we are so far from that, it's a struggle just to get the dining table clean and the dishwasher loaded and turned on every night. There are always clean unfolded clothes in our bedroom, waiting to be folded and put away. There are always stray toys around the house and stuff on the floor, here or there, things the kids had dropped. This past weekend, we totally completely sorted and cleaned out the children's bedrooms, it was a huge job. We took everything out of their rooms them put them back in specific sorted places, we even added labels to shelves and bins and some drawers to show where things belong. We're trying to get the children to help us clean before storytime every night and trying to guide them to clean up one toy or set of toys before they pull out another, making cleaning up so much easier. My children are 4 and 7 though, so not everyone can do this and yet probably, by this age, most people have their children already in the habit of cleaning up...somehow we missed that stage.
I think that one of my biggest problems is that I leave the cleaning until the evening, after the children are in bed, then I miss out on "me" time and "hubby" time, rushing to tidy things for the next day and then hopping into bed exhausted...only to be exhausted again the next day, when we go about our daily routines. My goal is to stop doing that, to regain some order, get up earlier perhaps and spend an hour in the morning focusing on cleaning and tidying, making sure that at least half an hour in the afternoon (after we get back from our daily adventures) is spent tidying or cleaning again. Then making sure that the kitchen and dining area are both clean after dinner, so that I can relax and enjoy the evening, worry free, after that.
For the OP, with 4 children, do you have one concentrated area that you could corral the children for half an hour at a time, or even 15 minutes, while you accomplish a daily task? Perhaps cleaning another room, or putting in some laundry? Do they play nicely enough for that? Could you work on instituting a more cohesive nap/quiet time into your day, so that say, two of the children are napping and the other two are having quiet time, playing quietly in one contained area so that you can get some work done around the house?