My mom created charts out of tag board that had columns with the the job adjusted for age level(pick up toys, make bed...etc). I always got mowing the lawn, why was that. When we completed them we put up the velcro piece. Each week if all our velcro pieces made it to the end of the week together, then we got to do something special. (like picking a movie at the video store, or sitting in the front seat, ...it doesn't have to spectacular).
She left them sort of general, so that pick up toys meant all toys, pick up clothes meant all clothes--dirty ones in hamper, clean clothes put away. If we didn't, then she started taking things away. She locked the tv in the trunk of the car for a week once. After a while of not having access to things, we started getting the picture. If you have to pick them up, then put them in a box and put it somewhere where they can't get them. If you end up picking up all their clothes and they have nothing to wear and have to run around in their underwear they may start getting the picture that keeping their clothes picked up is worth respect too.
It sounds like they lack a basic respect for what they have. If they argue, just cut them off and tell them your not arguing, this is the way it is, and if you have to do it then this is what is going to happen. No second chances. if they don't have any tubs of toys, they'll be pretty bored. Don't even let them argue. I find that picking up immediately, is better than later. Immediately has better association recall. If they come out of a room, send them right back in to pick up, even if that delays them eating lunch/dinner. My brother went to bed a few times w/o dinner, my sister lost out on getting to go to a slumber or birthday party once that even though it was like 2 weeks away, mom just took it off the calendar. I lost getting rides to school from her for early morning band...I had to walk or ride my bike and I was still expected to get there on time not just by her but the director. Riding my bike with a bass clairnet/tenor sax is not the easiest thing, but yes it can be done all while wearing a backpack of books.
The things they do or have are for them to take care of. our ancestors probably did not have 1/2 of what we do now and they generally lived well or we wouldn't be here.
Sometimes i think if kids can start developing and understanding for what's going on around them it makes them start paying attention more. You could create a calendar that shows everything that your doing. have family mtg night (Sunday) that goes through everything you/kids are doing and impress that if their chores don't get done then activity A will be "erased" from the calendar. My dad did that with us.
The first few times, I remember my dad standing in the middle of the room and we had to report back as we finished he would inspect.
Good luck. it's an uphill battle on a slippery slope, and you may feel like you don't have time, but it's worth it in the end if you can achieve it. And your kids will appreciate it later too.