You are correct to conclude that in order for you to have a satisfactory outcome in the above situation, both the refractive errors and strabismus have to be addressed. Ideally, we should conduct a full evaluation of your eyes to rule out any other eye-related problems.
Generally, refractive surgery should be performed prior to the strabismus surgery as the degree of strabismus may change after refractive surgery. This sequence would result in a more stable and predictable outcome for both conditions. The risk of performing the strabismus surgery first is that the strabismus may re-emerge after the refractive surgery. Strabismus surgery can be performed once the vision following LASIK has stabilised. This would ideally be a minimum period of 1 month.
The main precautions about having to address both these conditions are that a full evaluation of the eyes and strabismus is needed, the strabismus and refractive errors are stable and that there are no contraindications to having both surgeries.