These effects are what should be expected and welcome when taking substances that are intended to remedy disease at therapeutic levels.
Most people stop taking them because of the discomfort experienced resulting in their use being ineffective. And in some cases, I would suggest, making that which you are trying to overcome stronger.
Iodine – High iodine intakes can cause thyroid gland inflammation and thyroid cancer. Getting a very large dose of iodine (several grams, for example) can cause burning of the mouth, throat, and stomach; fever; stomach pain; nausea; vomiting; diarrhea; weak pulse; and coma. ~NIH-Office of Dietary Supplements
Neem Oil – Neem (Azadirachta indica), popularly known as traditional medicine is a native plant in India. Neem oil is a vegetable oil derived from seeds or fruits of the neem tree through pressing or solvent extraction, and largely used in popular medicine to have antifungal, antibacterial, antimalarial, antiparasitic, anti-inflammatory, as well as immunemodulatory properties in different animal species. In the present study, acute and 28-day subacute toxicity tests were carried out. In the acute toxicity test, the LD50 values of neem oil were found to be 31.95g/kg. The subacute treatment with neem oil failed to change body weight gain, food and water consumption. Serum biochemistry analysis showed no significant differences in any of the parameters examined under the dose of 1600mg/kg/day. Histopathological exams showed that the target organs of neem oil were testicle, liver and kidneys up to the dose of 1600mg/kg/day.
According to the math, that would mean that a dose of 4 ounces wouldn’t cause any harm . However, I would suggest that if someone had a deep seated fungal infection that they would experience a significant amount of discomfort.