Girl, with a 4 week old, you are soooo in the thick of the transition. Let your house rot :)
My DH also works long hours, and we have no family nearby. It's hard. I feel you.
One thing that helped me, during the first few months, was to think of things as "vacation time" not real time. Anything that got done around the house was bonus, not to be expected. My only goal was to keep up with dishes so there was no actual rot/insect infestation.
As far as the other kids go, you don't say what ages (other than under 6). I set up a shower curtain on the kitchen floor and make slime for DD. In the early days with DS, I would pull up a chair and nurse him while she happily got disgusting. I havent' made it in a while, but I want to say it's just cornstarch and water, and food coloring, because ours had to be pink :) Other things that kept us busy were putting him in the Moby and going to the playground or just on a nature walk. I was totally hands free for her, but he was sleeping and or nursing and happy as a clam. While taking care of little one, I narrated everything I was doing to DD, so that she wouldn't be left out. I'm changing his diaper now, can you pick which one he should wear next? Until she potty learned, the diapers had to match :) Since about 2 1/2, DD has rinsed dishes while I wash them. She also gets a spray bottle (filled with water) and cleans cabinets while I do other things in the kitchen. Or, sometimes, she has a tea party, and I sit with her and snap beans or cut veggies and talk to her while she sips "tea".
Other ideas: watercolor paints or food colored shaving cream and a paint brush in the bathtub. We "chase" each other down the hallway with toys that want to get put away. We do 5 minute cleanups, while playing loud kid music. Anyone who stops while the music is playing gets their belly "eaten". DD has her own "vacuum" and she vacs while I do. I chase DS with the vacuum, now that he's mobile- he finds this hysterical, but when he was little, he was in the Moby for chores. When DS was still wee, there were lots of stories while I nursed. She loves stories. Princess DD and Prince DS live in a castle on the beach near a waterfall....Great when I had no free hands for books.
For quiet time for you.....in the early days, DD was allowed to watch 1 30 minute DVD. While DS napped. As much as I am against tv, everyone gets a 30 minute break during their work day or they go INSANE. My DD was and is VERY clingy, so that was the only thing I could find to work for us. When DH is home, he knows that the only thing I want is 20 minutes in the bath BY MYSELF, and I am a happy camper. I have spelled this out for him bluntly. And I ask specifically, so that there's no misunderstanding. I don't think he truly has any idea how stressful constant childcare can be when you are by yourself, so I don't wait for him to volunteer. So, probably my biggest suggestion would be to find ways your DH can help you to get your needs met, and then be very specific (in a positive way, of course). I know my DH works very hard, but his co-workers don't cling onto his body and yell insane demands at him all day long, kwim?
Oh, and for food. Crock-pot. I used it almost daily during the early days. That, and cooked insane amounts of food at a time, so that we had tons of leftovers. Dinner-time was too crazy, and the kids too crabby to try to cook anything then. A huge roast with some veggies in the crockpot would make 2 dinners and a lunch or so for us. Boil a dozen eggs at a time(if you eat them), so that you have snacking food. My kids favorite snack is frozen blueberries, so I keep them in the freezer. If I have a minute where everyone is occupied, I'll cut up cheese into cubes for snacking.