Are there any in my world? Hahahahhaa, absolutely, yes! And they are much as you describe: strength, fangs, claws, unbelievable power and immortality. A monster, a demon is a creature capable of living forever and tearing other living beings apart like paper. But there's more than that.

These beings, these creatures of darkness, are completely lacking in soul and conscience. They are driven by an irresistable urge to destroy. They will butcher innocents without conscience. They will feed on blood, gorge themselves on other life. Even the immortal soul of their victim, they will corrupt or steal.

In accepting such power and becoming a demon, one forfeits all humanity! That is what I mean by 'monster.'