To me, Woody helps them survive because his positive attitude makes the bad stuff that has happened to them seem less serious.

For example, when they first get to Manzanar, they wake up and find that there is dust all over everything.  But instead of being depressed about that and about how little room they have, Woody makes a joke of it and gets people working that way.  (Like when he tells the younger boys they will eat any dust that is still left by breakfast time -- but at least they'll get catsup.)

So his good attitude makes it seem like the bad stuff isn't so bad after all.