Is it odd to never go to the doctor or dentist?

No: Many people avoid the doctor. Although it may be for $$$ reasons, often is the fear that the doctor may "find something wrong". But this is exactly what you want your doctor to do. As with any disease, when identified early the success of treatment increases while the cost and any negative effects are decreased.

It's not recommended: The body has a wonderful way of taking care of itself...Except for teeth. They need to be cleaned and examined by a professional to correct small problems before they become large problems. It's the same for general health items, by the way. A person needs periodic baseline studies (physical exam, blood pressure, blood studies, etc.) teeth need periodic xrays and examination by professionals.

Not odd but not good: The reason for regular periodic medical and dental exams is to find problems when they are small, easier to treat, and less expensive to "fix." by the time something hurts, it's advanced. Please do yourself a favor, have regular examinations. Better than the alternative.