For those of you who are trying to express sympathy or communicate how moved you are by the cuteness of something, it's "aww" and not "awe." Unless that new puppy / kitten / baby inspires respect mixed in with a healthy dosage of fear, it's "aww." And it's most certainly not "awl*," unless you want me to use one on your face. K, thanks!
*Awl - A small pointed object used for piercing holes, esp. in leather