What kind of home treatments will cure oral thrush and how long will it take for it to be actually cured?

None. Thrush is treated with topical antifungals to the mouth. These are nystatin (mycostatin) liquid suspension-swish and swallow 4 times a day or Clotrimazole troches-dissolve one in mouth 4 times a day until the lesions are gone. For resistant cases fluconazole (diflucan) 100-200 mgs. Orally once a day for a few days will usually work. I know of no home remedies that work for thrush.