You don’t say how old the boys are, but I’m guessing they are rather young. I have two boys, a six year old and one that will be five next week. They are insane, and I can only imagine what it’s like to live with three boys!
First, I think it’s very important that you sit them down and talk about the rules. Explain that your job as Mommy is not to clean up after them. Make a poster of rules if you have to, with the rules as pictures instead of words if they can’t read yet. Then, enforce the rules.
If my boys make a mess in their bedrooms, they aren’t allowed out of their bedrooms until they are clean. They will get mad and throw a fit, but I calmly remind them, “It’s almost snack time. Just get it done so you don’t miss snack.” Since they are rather young, I will help them pick up the toys only if they are helping too. The minute they start to play or sit around instead of helping, I tell them they are on their own. Sometimes it helps to give them directions so the job doesn’t seem overwhelming. I’ll say, “Pick up all the Legos first, and when that’s done we’ll work on something else.” Breaking the job into smaller jobs helps them not feel like they will never be finished. It’s important to stick to your guns. They are used to getting away without helping, so they will not instantly fall into line. They will test you. Just keep reminding them, “You made this mess so you get to clean it up.” I do not give them an allowance or anything for cleaning up their own messes. I do praise them for doing a good job when they are done.
As for the toys, you should certainly take away things they are misusing. I even explain to my kids that we work hard to have money for things they want and we will not replace them if they are broken. If they can’t play with toys in a way that doesn’t risk injury to our house (or each other), I put the toys away for at least 24 hours. If they get a toy back and continue to abuse it, it gets taken away for longer.
I think you should pick up some inexpensive dressers. If the clothes are put away, the kids can’t mess them up. They can also help sort and put their clean laundry away. Give them some responsibilities to feel good about. Both of my boys are responsible for putting away their folded laundry (although I do help the youngest because his dressers are old and difficult to open!).
As I’m typing, I’m reading the responses above. It sounds like the biggest problem is that your boys know there isn’t going to be any follow-through with discipline. Nothing you try will work if you are inconsistent or if your husband isn’t on the same page. Things will only get worse as the kids get older. Seriously, what you need to do are set ground rules according to your priorities as a family and stick to them like glue. There is no magic cure for getting kids to behave overnight. You’ll all need to change your habits.