What could be the reason for often (several times a week) strong headaches with no apparent triggers, that sometimes go away with paracetamol?

Could be anything: Headaches could be due to simple viral infections or major brain tumours. It is difficult to say without more information and examination. It could be a tension headache, a viral infection, migraines, due to poor eyesight, meningitis or a haemorrhage. In short you need to see a Dr who will take a history and perform an examination, if needed you will be referred for a CT scan as well.

Can't be exact about: The cause of headaches because there are several major types, e.g., vascular, sinus, muscular, tension, etc. Please see you doc so he/she can examine you and give you the proper treatment for the type of headache you have. Sorry you are dealing w/this. Peace and good health. Nutrition and biofeeback are some natural approaches after you've seen the doc.