I looked them up in a Japanese dictionary. Here are some of their meanings. 無理 1. irrational, 2. impossible, 3. overdone 駄目 1. useless, 2. ineffective, 3. impossible, 4. forbidden As you say, both of the two words have a meaning of impossible. In this case, they should be interchangeable (there may be a difference in their nuances, though). Regarding 無理しないで, this would be associated with 3 in the above. The following URL is the Japanese dictionary, where you can see some examples. https://kotobank.jp/word/%E7%84%A1%E7%90%86-642522#E3.83.87.E3.82.B8.E3.82.BF.E3.83.AB.E5.A4.A7.E8.BE.9E.E6.B3.89