Is malice a strong feeling?

Yes it is

Yes, it's a very strong feeling. To have malice for someone denotes a desire to cause injury, harm, or suffering on another person. Reasons may be impulsive or premeditated and come from hostility or pure meanness........ it's an intense feeling of dislike.

mal·ice (m l s) n. 1. A desire to harm others or to see others suffer; extreme ill will or spite