S.O.S. . . .I have a sock problem

I just found 7 (not kidding) children's socks in the bathroom and 4 in the living room-- a few matches, but mostly singletons. I haven't checked downstairs, but I am sure there is also a pile there. My kids take off their socks every time we walk in the house. Then, they put on a new pair when we are headed out later. Again, it is another pair at bedtime ("mom, I don't want cold feet in my sleep!-- "ew, those ones are dirty!"). I used to throw the socks in a laundry bin when I found them, but then I couldn't wash the clothes fast enough to have clean ones. Now they are left littering the house. It has gotten so bad, that the kids have now started wearing "rainbow socks" (dubbed by Davis). Rainbow socks are unmatched socks. The kids will just pick up a sock whereever they find it and put it on when I am shouting for them to get some shoes and socks on so we can walk out the door. The twins have also started hiding socks behind couches or corners when I ask them to please take their socks back to their room. To top things off, Eliza has started raiding ROGER'S sock drawer when she can't find any of her own (isn't it really unnatural that she can actually fit into them?). I literally can't keep up with this mess!! Any thoughts, suggestions, or otherwise? I am drowning in socks here!