Broadly used for the effect or influence one thing has on another, whether physical, social, psychological, or abstract. Often used with ~を与える, ~を受ける, or as a する-verb.
影響 is the general, neutral word for any influence or effect, while 煽り in this sense stresses an indirect, often negative knock-on impact from some event.
影響する is a general, everyday way to say something 'influences' something else, while 及ぼす is more formal and stresses actively exerting a concrete effect or result.
影響 is a neutral word for being influenced by something, whereas the suffix かぶれ implies a shallow or pretentious kind of influence that invites criticism.
影響 is a general influence or effect one thing has on another, whereas 反響 specifically describes the reaction or echo-like response that follows an event.
影響 is the general noun for 'influence' or 'effect' itself, while 波及 describes the process by which that influence spreads outward to affect other, often unrelated, areas.
影響する is the neutral, broad word for having an effect or influence on something, while 響く suggests a more direct, felt impact, often physical or emotional.