I never thought Everway was weird. I still don't think the setting is terribly unusual. But the mechanics... I can see it. The author was trying something, a game where trust in the GM was a vital part of resolution. The mechanics as written explicitly require the GM to make a lot of decisions. Decisions I think a lot of GMs make, but in Everway, these choices were baked into the rules of play.
Cards were NOT the key mechanic in task resolution. A lot has been said of them in other threads, and I love the concept... but really the cards were written to be the backup mechanic. Task resolution relied first on whether the GM thought you reasonably could succeed at a task, then whether or not you should succeed by the beats of the unfolding story. If neither of those suggested a clear outcome, then the cards would come into play. A card drawn from the fortune deck would be interpreted by the GM. This could be as simple as good/bad, but the GM was encouraged to apply the cards' meanings, elemental influences, astrological influences, and other things, all to decide whether or not you sweet-talk that guard...