Why I cannot say "他坐着在沙发上看报纸“？
着 is a strong termination mark for an adverbial clause.


  他坐着吃饭 = 他 / 坐着 / 看书
  
  他笑着回答 = 他 / 笑着 / 回答
  
  他哭着跑开 = 他 / 哭着 / 跑开


着 here terminate the whole adverbial clauses.


  你哭着 you crying + 你对我说 you say to me = 你哭着对我说 you say to me in tears


One can easily separate out 哭着 because it's a whole.



Back to your original question, 着 has to be at the end of the clause, and hence 在沙发上坐着 (not 坐着在沙发上). It will be understood as


  他 / 在沙发上坐着 / 看报纸。


However, the sentence is also grammatically correct if you add a comma after 着. It will sound like there are two predicates rather than one (modified by an adverbial clause).


  他坐着，在沙发上看报纸。
  
  He is sitting, and reading newspapers on the sofa.


In general, anything that belongs to an adverbial clause should go before 着.



One exception though is when the verb is transitive.


  孩子 / 抱着妈妈 / 哭了起来。 Hugging his mother, the child started to cry.


In this case, the object can be put after 着.