What would happen if I take prenatal vitamins, birth control pills & iron pills at the same time?

Nothing bad. Vitamins are vitamins. Iron is iron birthcontol pills are just that. They can all mix just fine.
?upset stomach. There should not be any medical reason you can't take all three simultaneously if you can tolerate them. Since any of the three can cause nausea it may be more likely if all three are taken together.