"Put on clothes" means clothes are moving onto your body :)
You wouldn't say "take on clothes". "Take on" is usually used in the sense of adding more, especially more responsibilities to your life, such as "taking on a second job", "I'm taking on more hours at work", "the teacher is taking on more kids in the classroom", etc.
Again, with the "adding to" references I made, another situation: you're in a boat on a lake, and the boat begins sinking and you can't stop it...you even send out a distress call :O You tell them 'My boat's "taking on" water.'...I suppose because in a sense, the boat is "taking" water from the lake, but anyway... :)