**** Etymological explanation
- 無理: 理が無い(ので達成できない)
you can't acieve it because it is unreasonable
- 駄目: it makes no difference (やっても無意味、無価値)
This word originates from GO (囲碁) game,
駄目 in 囲碁 means "useless/worthless slot", which turns to mean simply "useless/worthless".
*****
However, nowadays 駄目 is often used to express prohibition, "Don't do that"
「だめ、来ないで」
「薬物濫用。ダメ!ゼッタイ
http://www.dapc.or.jp/」
you usually use むだ to express "worthless/useless even if you try".
**** example
このプールは深いから、子供が泳ぐのは無理だ。: A description with a reason.
Children can't swim here because they are small but the pool is deep.
このプールは深いから、子供は泳いじゃダメ : A prohibition
Children is not allowed to swim here because it is dangerous.