I agree with this.
The problem is how to apply the non negotiable routines and job list so that they actually take notice and do something.
The DH has set a horrible example to the kids.
They have seen him take no notice and so have decided they don't need to either.
Also if the OP is at the end of her tether, the sheer amount of energy it takes is overwhelming. When you finally round them all up to sit down and talk to people who will either not listen, say that you are nagging (implying unreasonable and not worth listening to) and that it doesn't need doing anyway and that you are making a fuss about nothing so nothing happens. They will also if they've been observing the DH/DP use counter arguments - "Well you do xyz!!!" and three male teens can make a lot of noise over talking. It could get very heated.
So I also agree with the previous poster saying OP needs to ask for help from GP and others to help her cope.
OP I actually think you have set up some really good routines already with the shopping etc But its not easy and its an uphill task communicating with people who've been taught not to listen.
Can you get DP to go and stay with relatives for a while? Having him and his personal mess out of the house would work and might shock your boys into listening to you. I also think it would be easier to gee them up without him there unless he sees a point in helping. His bad example has helped create this.
Other Ideas
VISUAL AIDS Take Photos.. of the worst of it. They cannot say.. "You are exaggerating or claim its not true. Maybe produce a list of the jobs you do in one column and the jobs they do in the other. Or do a chart of how much free time you have... and how much they have. A pic after you've just cleaned it, compared with one they've messed up
Talking to them in a cafe..ie not in the house where they are watching tV. They will all be sitting at a table.. at eye level., full attention they won't get food if they walk off..Make it lighthearted (even though you might feel like grinding your teeth) ie Don't make it miserable to have these talks, say to them I want to speak to you like the adults you are becoming.
eg. Maybe ask them how would they like to improve their room. What are their ideas for how it could be better. What's the first thing they'd do. (then Produce a picture of their room looking terrible and what's the first thing they'd do) Carrot rather than stick.
eg. Maybe produce a list of the jobs you do in one column and the jobs they do in the other (which won't be many) and ask them how would they reorganise to make it fairer.
I think the key is getting them to say what they think about a specific beef, and get them discussing it, get them to come up with a solution, rather than letting them come back with the standard "no" talk.
eg EG. With the one you make responsible for emptying bins... if they start with its not necessary. Ask them what happens when the bin overflows. Who do they think should empty the bin. How long do they think the job takes. Is that reasonable. What is their solution to improving the situation..OR.. Tell me how you think we can all help you to get out of bed for school. What specifically do you find difficult. What do you think would work ( football Klaxhorn probably) . Or if there are 4 people in the house. Who should do which of this list of chores? What chores could you do to help?
Could you get a friend or family member to come and give you a bit of a hand with decluttering.
A place for everything and everything in its place.
Go baskets. for gathering all their stuff off the floor to go to their rooms. If overflowing put it on their bed.It's their problem. Go bowls/bags where they dump their keys, entry cards, anything they need for the next day as they come in.. so there's a place they can look for themselves. Their own labelled hook to hang their school coat etc. but they need to eat at the table.. scrape their plates and put in the DW.. A pop up basket for each of them for laundry, If its not in front of the washer, it doesn't get done.
Labels and post it notes (or as they like to call it "Pass Ag notes" ) eg.. pinned near the bin "Please take the bin out by Tuesday"
It won't happen over night try one new task a week, with a reward. Give it a chance. that's not working, maybe try more drastic action. I also think letting DH and all of them to just get on with it for a weekend.
I'm sorry you are having such a hard time, I would look at this as step by step small tasks... and keep chipping away. But also get some real life support if you can. Best of luck OP x