What Jesus said about evil
Jesus had a very real sense of the presence of evil in the world. Christians don't always see eye to eye on how personal this evil is but they all agree that evil is real and something to be resisted.
Jesus often spoke about satan and demons
Jesus himself described evil in very personal terms. He talked about the devil and about demons. He was often called upon to drive demons away and left us in no doubt that he had supreme authority over demons even if the demons themselves like to make mischief.
Evil is not equal to God
Jesus wanted us to understand that no matter how evil the world might seem God is greater. He was very clear that there is only one God and that God is good.
So why does God allow evil
This is a hard question to answer in just a sentence or two and ultimately this is a question that only God can answer. However we do know that Jesus accepted a very evil act being done to him and that through this act something great happened. I'm talking about the crucifixion, of course, more on this later.
So we know that God has direct experience of suffering so if God allows it then it must be for a very good reason. If you ever have to suffer then it can help to know that God does not leave us when we suffer but suffers with us.
Perhaps the best answer to the existence of suffering is that it is a result of us having free will (the right to decide about our relationship with God) and that this is something that we share in collectively and is not a punishment for individuals.