Is strabismus curable in a 24-year-old?

Yes. Strabismus is eye misalignment. There is no particular limit in age for treatment.
Depends. This depends upon what you consider "cure". If one of the eyes is amblyopic (lowered vision from childhood) this cannot be improved. If the eyes are misaligned, they can be surgically straightened at age 24 but this will not change the vision. Discuss with your ophthalmologist what your goal is.