I see that both eikyou and kouka mean effect..
Could someone please explain to me the difference and when to use both with possibly a few examples?
効果 usually refers to positive/beneficial effect. 効果的 always means "beneficial/effective". 視覚効果 means "visual effect". When people refer to the good/expected effect of a medicine, they normally say 薬の効果 (or 薬の効能).
影響 is a neutral word and it can refer to a bad effect/influence, too. 彼に影響された means someone was influenced by him (either positively or negatively). 薬の影響 tends to refer to unexpected side effects.