The sentence "He clasps the crag with crooked hands" employs a figure of speech called personification. Personification is when an author gives a non-human thing - an object, an idea, an animal - attributes or features of a human. In this case, the pronoun "he" is being used to refer to an animal even though the correct pronoun would be "it". Also, the author chooses to use the word "hands" - a human body part - to refer to the eagle's "claws".
Notice how the word soliloquy is a bit like the word 'solo'. This is basically what it is: a solo in drama, where somebody is projecting their inner thoughts. This gives the audience direct access to the character's feelings.
