Oh goodness L., you do need help, but that's not always available when you need it, so what do you do.
I would suggest you make use of gadgets.
Meals: Since you are alone in this, select quick meals that you can use a slow cooker. It cooks while you do stuff.
Attention/Family time: You know the 6yr old is severely handicapped, so once you make him/her comfortable, you can have her in the room watching while you play with both of the other small kids, or you all can do the peekaboo, jumping, painting games together..
Chores: Make use of high chairs, booster seats, crib, playpen, etc to keep the younger ones secured while you do laundry, dishes, or whatever.
You time: Sleep when they are sleeping, sit in a sofa bed if you have one with the 7mo old while you have the 2yr old watching an age appropriate DVD,etc.
Wish I could offer you some more solutions, but try to make it easier on yourself by taking it one day at a time. Don't be too concerned about the mess, you cannot help it right now. Find a space you can make YOUR getaway space and do the other chores when you get a chance to do so.