How long is it supposed to it take for my eye to heal from strabismus surgery?

Up to a month. It depends on what you mean with healing. Closure of the incision takes a week or so. The final position of the eye may take a month. The redness gradually fades over three or so weeks. Re-operations may take longer.
Weeks to months. It can take several weeks for the redness and appearance of your eye to get back to normal. As far as correcting your double vision, this can sometimes take longer as the muscles, nerves, brain are trying to reconfigure themselves. The key is to maintain good follow-up with your surgeon so he/she can monitor your progress and decide if repeat surgery is needed as can be the case sometimes.