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!