My daughter (12) and I both (but independently, apart from each other) came up with the following solution: You object to 2 things: clothing on the floor, and your having to determine what's clean and what's dirty. Go into their room(s), take EVERYTHING you find on the floor, put it into a large leaf trash bag, and hide it. If it's in the hamper, it will get washed. If it's on the floor, it disappears (not permanently, but just enough to make an impact). If they have to go to school wearing the same thing for a few days, peer pressure will get to them. And if they put clothes on the floor while they take a shower, those will disappear, too; you might need to be willing to have them skip school for a day due to nakedness (decide beforehand just how far you're willing to go, and then HAVE NO QUALMS ABOUT GOING THERE.
(It's like when moms are told that if they threaten, they have to be willing to go through with the threat: "If you don't stop doing that, we'll leave the movie right now"--well, OK, but you've got to be willing to do that, otherwise the kid knows it's an empty threat.
I have had this issue with my daughter, and this gave us an opportunity to discuss it. I like involving her in decisions I make concerning house rules (she decided what is an appropriate time to shut off electronics such as cell phone, Ipod, computer, and she self-monitors this, so I'm relieved of the job of nag. I also had her decide--with some guidance on my part--punishment for infractions).
When she was about the age of your boys, she did the same thing. Her father (my EX, and this is indicative of why he's my EX) took all of her clothes except what she was wearing (no discussion beforehand, just did it suddenly), and told her that if she put those away for 2 days, she could have another set of clothes. She cried considerably, of course, but did eventually "earn" back her clothing. I would definitely NOT advocate that method; it still seems very unfair.
You might want to warn your boys beforehand what you'll be doing, or just let them realize that their choices of clothing is dwindling. But if you want to keep their rooms neat but not nag and not have to decide what's what, remain calm as you scoop up armsful of clothing and chuck it in a bag. Later they can help you do laundry.
Best of luck.