Oh, I hear you! I have one, and he was impossible at this age. First of all, "clean your room" can be overwhelming at this age, particularly when it is such a disaster that they don't know where to start. Separating it into tasks like clothes, books, dolls, etc. can help. You could try separating them - one in the shower while one does clothing, then the other showers and the clean one does books. The other thing I did with my son was to take away privileges - it DOES work if it's immediate, but it doesn't work if it's delayed. For example, "Clean now or there's no TV tomorrow" is too delayed at this age. Instead of you being the maid, try taking away an entire category of things that make the mess. For my son, it was dinosaurs and hot wheels and legos. I couldn't walk in his room without stepping on something that hurt! So, I packed everything in boxes and put it all in the attic - I left him with stuffed animals, his special blanket, and books. Everything else went in the attic - "Since you didn't take care of it and it doesn't seem to be important to you, I put it away until you are older." THAT got his attention. Same thing worked for safety - the first time he rode out into the street without a helmet, the bike went up in the rafter hooks in the garage - he could see it every day, but he couldn't ride it. That was a long week, but he didn't ride without a helmet again. Once he rode into the street without looking for cars, and up the bike went again. Never happened again.
Reducing the amount of stuff in the room will reduce the clutter - if it's all over the place, they aren't playing with it anyway. And you're probably doing twice as much laundry with clean clothes winding up on the floor and being walked on until they are dirty. However, you can also pack up what it on the floor so they won't have it to wear. No one ever suffered irreparable harm by wearing the same outfit 2 days in a row.
If your girls have specific storage areas, great. If not, it might help to create them - books in one area, etc. Then label them. Before my son could read, I put pictures of the items on the storage bins. I gave him a drawer unit to hold construction paper, markers, crayons, etc. - and each drawer had a picture so he could tell what went where without opening the drawers to look. That saved a lot of time, and set up good habits for studying/homework later on.
The last thing I would say is, they are not listening because they think it's hilarious. You are right that some things are funny if you aren't so exhausted or distracted - and they know innately to do this at dinner time when it will push more of your buttons. But the only repercussion is you being upset, and that just sets them off - they enjoy being "in control" after a day of being at school and following rules.
You could try a chart with whose jobs are whose on which days - my neighbor does that with her 2 girls - one does the dog, the other the guinea pigs, then the next day they switch. If they get stickers, they get an allowance. If they don't cooperate, they still have to do the jobs but there are no stickers/allowance. But you are right, you don't want to create a situation where they expect money or a treat every time they just do what they are supposed to. Rather than rewards, try deprivation! This works great when they are older too - taking away the car from a new teen driver works wonders!
In any case, you are in the driver's seat - where you should be.
Good luck!