score:6
Short answer
Yes, God is love. Yes, God and Jesus hate evil. Yes, overcoming evil is why Jesus came. But in our actions, like Jesus, Christians should NOT be driven by hate but empowered with love. For strength, you may have been thinking of anger, an irascible passion that can be in the service of both good and evil action (see the analysis below).
Detailed answer
In Catholicism, using the Thomistic analysis of the human action, while hatred (being one of the 6 concupiscible appetite) can be a cause of an action aroused by evil it's not hatred that makes you stronger, but a combination of:
which plug into appropriate stages in the Process of Human Action:
Concise descriptions of each of the 11 passions by Notre Dame Thomist expert and professor: Alfred J. Freddoso
Aquinas 101 topical videos
Aquinas 101 Course 4: Principles of the Moral Life:
Peter King's book chapter Aquinas on the Passions in Aquinas's Moral Theory (Cornell, 1999)
Peter King's book chapter Emotions in Oxford Handbook of Aquinas (2012)