Is it normal to wake up in the morning with headache and nausea?

Morning headache: No. Poor sleep often contributes to headaches, because of the small muscles that attach the head to the neck. Nauseating headaches sound like migraines. I'm assuming you aren't overdrinking alcohol. Work on sleep hygiene: more exercise, less caffeine/alcohol, power off tv and computers before you go to bed, and avoid naps.

No, it's not: It is not normal and you should see your doctor and talk about these symptoms. Often times people who clench and grind their teeth while they sleep can wake up with headaches but this would not cause nausea.