How does Lord Rama's behavior towards the demonness Surpanakha compare to Odysseus's behavior to Calypso and/ or Circe? What does the behavior of...

Odysseus and Lord Rama display significant differences between the way they react towards temptresses.

In The Odyssey, Odysseus does not forcefully repudiate Circe and Calypso. He stays with both of them.  While he does leave eventually, Odysseus does not immediately reject their overtures.  While he could be seen as having been "captured" by both, it is difficult to see how, if he truly wished to be free, he would not have been able to...

Odysseus and Lord Rama display significant differences between the way they react towards temptresses.

In The Odyssey, Odysseus does not forcefully repudiate Circe and Calypso. He stays with both of them.  While he does leave eventually, Odysseus does not immediately reject their overtures.  While he could be seen as having been "captured" by both, it is difficult to see how, if he truly wished to be free, he would not have been able to extricate himself.  Odysseus decides to leave both temptresses after staying with both of them over a period of time.   He eventually rejects both of them to go home to Penelope. 

Lord Rama is steadfast in his refusal towards Surpanakha. Lord Rama does not ever entertain being with her.  He is resolute in his rejection of her.  It is for this reason that she goes to her brother, Ravana, for revenge.  Had Lord Rama acquiesced to her, she would not have been so angry and so insistent on revenge. 

Both heroes face temptation from women who are not their wives.  However, their reactions to these situations differ. Odysseus might have stayed with Circe and Calypso out of guile.  He knew that in order to go back home, he had to avoid their wrath.  He might have stayed with them to avoid their anger, displays that could prevent him from returning home.  He might have also stayed with them out of sensual enjoyment.  

Odysseus's willingness to stay is fundamentally different than Lord Rama, who is forceful in rejecting Surpanakha. Unlike Odysseus, Lord Rama does not reason his way out of the situation.  He simply insists that he will not stray from his duty as a husband.  Lord Rama suffers for his adherence to dharma.  Surpanakha's anger at Lord Rama's refusal ends up causing her brother's involvement and the kidnapping of Sita.  Odysseus is pragmatic, looking at the end result as the most important element. Lord Rama is staunch in his adherence to duty, even if it results in his disadvantage.