Final answer:
The inferior oblique is the muscle that attaches to the posterolateral part of the eye and is responsible for elevating and laterally turning the eye when it contracts.
Step-by-step explanation:
The muscle that attaches to the posterolateral part of the eye, elevates it, and turns the eye laterally is the inferior oblique. This muscle is responsible for the external rotation of the eye, working opposite to the action of the superior oblique muscle.
When the inferior oblique muscle contracts, it helps in the complex movement of the eye by elevating the eye and also by rotating it laterally to counteract the pull of other muscles like the superior rectus. This action is essential since the superior rectus pulls the eye at an angle, requiring the inferior oblique's intervention to maintain proper alignment. The nuanced coordination of these muscles also involves the innervation by cranial nerves, particularly the oculomotor nerve for the inferior oblique muscle, which coordinates eye movement and is crucial for tracking and locating visual stimuli.