My 4 kids are all under age 10 and we refer to the baby as the "one baby wrecking crew" -- at 13 months, he's into everything. I have trouble concentrating when there is a mess, so I enlist the help of the bigger kids and try (ha ha) to make it fun: "Everyone pick up 5 things" or "Spend 2 minutes picking up this area." I find if I can send everyone upstairs for 10 minutes, I can get the downstairs semi-picked up. Then, of course, there is the upstairs mess. . .
I have to mop floors and other major stuff after everyone is asleep, though. Even little things like spending 3 minutes wiping down the bathroom while watching the kids in the tub helps. And baby wipes work OK for that -- they don't sanitize, but at least they won't irritate your hands.
Just keeping up with the laundry by doing some daily helps keep me from getting too overwhelmed. I find that when I get overwhelmed, I can't even get started, and then it just gets worse and worse.
I don't know if that helps at all . . . but it may help to know you are not alone in fighting the mess/clutter battle!