I'm sorry to hear this. My radiation treatment was delayed in 2011 do to dental issues, and cobra insurance coverage to have the work done, which consisted of several root canals, fillings. Even with no teeth extractions I had to wait several weeks before beginning radiation. You'll have to discuss with your RO and MO if the additional teeth should be repaired/ removed before beginning treatment if there is already a concern with their health. As far as radiation with teeth extractions that will be in the radiated field, it shouldn't commence until 14-21 days healing time, to reduce the risk of Osteoradionecrosis later on.
As far as IMRT, they are able to dose paint, and can avoid, give less dosage to critical structures like the salivary glands, if possible. There are three major salivary glands, and hundred of minor salivary glands in the mouth and throat, so they might be able to recover, and later compensate for any loss. If one side of the head and neck is radiated, the other salivary glands on the opposite side will be preserved, and continue salivary flow. Radiation also effects thin saliva only, not thick, and is why we get the rope or thick mucus later on until salivary flow start producing again or others compensate for the loss. Thin saliva is mostly produced in the parotid gland. The other two major salivary glands produce a mixture of both, but a lesser extent of thin saliva. Usually the parotid gland, if radiated, and if possible without tumor risk, is radiated at 26Gy, and the radiation volume less than 49%, so it can later recover some saliva flow.
It's not discussed that often, but chemo can also damage the teeth and gums.
Hopefully there was already a discussion about impeccable oral care during and after treatment, use of fluoride trays, prescription fluoride, mouth guard during radiation to prevent scatter, and oral rinses. There are also prescription salivary stimulants, and OTC dry mouth products that may help.
Good luck.