Teeth rotted to almost the gum. Foul taste in mouth?

From Bacteria. The bacterial in the infection causing the teeth to rot will cause a foul taste in your mouth. Are you planning to have them pulled soon?
Yes. Its time to get to a dentist. Evaluate what your options are. Those rotted teeth could be makeing you sick and sometime dental abcesses are life threatening. There have been many advances in dentistry that make it more comfortable to get caught up. That foul taste is likely bacteria and infection.. Call a dentist tomorrow.