I was wondering is it normal to feel strong pain during a root canal?

No: Usually there is no pain at all when having root canal therapy. On rare occasions, it's hard to get a tooth completely numb at first. This is usually when an acute infection is present. There are methods to handle this.

It is not normal: Some soreness AFTER a root canal is normal. In most cases, you will not have any pain during a root canal procedure. If you have discomfort or pain during the procedure, let your dentist know and he/she will add more of local anesthetic to keep the comfort zone.