First of all, get your husband involved. Tell him how you feel and come up with a plan together.
I suggest that you hire a cleaning service, even if you just do it once. Ideally, you would hire an organizational service first, to help you sort and get rid of lots of stuff, and then you could get the house cleaned after that.
If you can't afford either right now, then hire a babysitter to come in regularly (once a week for 5 hours? daily for 2 hours?) so you can clean.
There are a few key things to keep in mind: Get rid of stuff, find a place for EVERYTHING, do at least one daily trip through the house.
You can't have a neat, organized house without getting rid of stuff. Don't just go to Target and buy lots of cool tubs to put things in -- be ruthless and get rid of as much as you can. Baby stuff you won't need anymore? Get rid of it! Keep doing it; as soon as the baby outgrows things, get them out of your house, either by selling, trashing, or donating. Clothes you don't wear, kitchen gadgets you don't use, paperwork from 6 years ago, jars of ancient who-knows-what in the pantry -- get rid of it all.
(My husband goes through the house thoroughly before our 2x a month cleaners visit and finds stuff that we don't use anymore to get rid of. I go through all of my clothes and the kids clothes twice a year and find tons to give away. We have a designated spot in our basement for bags of stuff to give to ARC.)
Next, once you have cleared the clutter and you have space, find a place for everything. And I mean Every. Single. Thing. We have a place for the kids' sunglasses. Baskets for each person's summer hats. There is a pair of scissors in the art cupboard (part of our dining room built-in) for cutting paper. In the kitchen knife block there is a pair of scissors for cutting food packages or other food items. In a drawer there is a pair of scissors for cutting open packing tape from big packages, or for opening clamshell containers. If you need to, label the spots.
I knew someone whose kitchen table was unusable because it was the dumping ground for newspapers, purse, backpacks, and anything coming into the house like shopping bags. She would not have had this problem if she'd had a place to put her purse, a place for newspapers, etc.
Next, you have to maintain. Do a walk through every room of your house at least once a day. (I do it once mid-day, and my husband does it in the morning and again at night.) You'll always find little things to put away, or notice things that need to be repaired or replaced or whatever.
Remember your husband? You can't do this without him. Your plan for getting the house in shape has to involve him. It's his house too; what will he do daily to keep the house clean and organized?
Good luck. You are in one of the toughest stages of motherhood -- three under three!!! Give yourself a break and don't be hard on yourself.