Evenly Matched and Cosmic Cyclone
So basically given that my Cosmic Cyclone was able to stop Imperial Order's effect from resolving, could Cosmic Cyclone also be chained to Evenly Matched and stop IT from resolving it's effect?


No you can't

The thing is that you were able to prevent Imperial Order from resolving its effect because it is a Continuous Trap card. In Yu-Gi-Oh some cards need to remain face-up to resolve their effects; continuous spell and trap cards are one of those (field cards also).

This means that you can "negate" (do note that you are not negating, but instead preventing from resolving) cards like Fire Formation - Tenki with cards like Cosmic Cyclone or the classic Mystical Space Typhoon.

The thing is that Evenly Matched is not a continuous card so even though it is banished or in the GY when resolving it will resolve, as you did not negate it's activation. 

A common example (and mistake) similar to this is when unexperienced players think they can "negate Dark Hole with Mystical Space Typhoon", when you can't as Dark Hole is not continuous and MST does not negate.