Does vitamin d deficiency cause severe itching and eczema in hands and legs? or could it signify an issue with the liver?

No: Vit D deficiency isn't a cause for eczema/itching or a cause for liver disease, can it be seen in people having those conditions? Yes, but not a cause. Vit D deficiency is usually related to insufficient vitamin D intake or insufficient sun exposure, a very common condition can lead to osteopenia or osteoporosis, (weak bones) if long standing, treatment is easy, good luck