Can an asymmetrical jaw affect the facial bones and eye socket?

Asymmetry of the jaw itself should not cause issues with the cheek bones or the eye. This constellation of findings suggests that you may have a craniofacial anomaly of some sort. This could be something such as hemifacial microsomia. I would suggest seeing a craniofacial surgeon for a proper assessment.

It may happen that multiple facial bones are affected in a process of facial growth and, as a result, one side of patient's face may look significantly smaller. Correction can be achieved with facial implants, fat grafting, fillers and, in more severe cases, free tissue transfer in the form of flaps. Hope this helps.

You did not post photos, but yes, the whole half of your face could be different from the other half. Detailed X-rays could be done to see what options you may have if you wish to improve your bone structure.