Well, believe it or not, we have already made progress!
Dinner is settling down. I laid out the rules, and one of went to bed hungry the other night. Noone died.

I have cleaned up with a garbage bag before. However, I usually do it out of anger, which is not a good way to discipline. I made it very clear that I will do that every night after they go to bed. If they would like <whatever> to be here in the morning, they need to pick it before bed.
Yesterday, I asked the younger to help me with the dishes. He was eager to help! I guess I hadn't expected enough out of them, because he did it right away. He unloaded the dishwasher and put away everything he could reach (he's only 6, can't reach the top cupboards.
The meals and the toys were my two biggest sources of frustration, so since we have made progress in a few days, I have hope that I can undo the mistakes we have made in the past.
I just have to stay consistent, and we should have these two habits broken in a couple weeks.
Then we will move to the next problem.
Which is arguing/fighting between themselves.
Which drives me crazy.
But... one battle at a time!
Thanks for all your suggestions and support!
Have a Mickey day!