In Life of Pi how do Pi's religion and storytelling play a factor in his survival?

Both Pi's dependence on religion and his affection for
storytelling help him to survive because they provide an element of escapism for him. 
Pi went through a terribly traumatic experience, one that should have emotionally
scarred him beyond repair.  However, because he was able to introduce the entire
experience as a story in his mind--one that involved Richard Parker doing all of the
dirty work, and the animals being the ones that were inhumane--he was able to survive
it.  He was able to pretend that it was all just a grand story, instead of a horrifying
reality.  That helped him to cope emotionally, and go on to live a normal life.  It was
a defense mechanism for his psychological health.

Pi's
religion was helpful in the fact that it gave him something to cling on to during the
tough times on the lifeboat, and to add meaning to his life after the incident.  His
religions provided explanations and comfort regarding his family's death and where they
might be afterwards.  Pi's reliance on three different religions also set him up well
for the love of stories, and the use of them as a way to make sense of our world.  That
is exactly what he did with his lifeboat experience--created a reality that made the
experience bearable.  Pi had already been practiced at being faithful in those
religions, so it wasn't too far of a leap to be practiced at believing his own version
of the events.

I hope that those thoughts helped; good
luck!