I know that Galactic Readiness defines how the game will end, but does it have an effect on the rest of the game as well? For example, if I played a ton of multiplayer and got my readiness up to 100%, would the dialog change so that everyone was commenting on how well we were doing? Would the map or mission locations change at all?
It changes a few things up to the ending. Like % of hammer that arrives on the surface and etc. Having certain people alive allows you to talk to them and makes a difference in endgame scenarios.
But other than that, readiness does nothing to change pre-endgame plot because your fleet power only matters when you use it.
No, the only thing Effective War Assets change is the ending. They are only taken into account when you start the mission Priority: Earth.
You could kinda/sorta say that having certain war assets changes the game - for instance, having Grunt or Jack survive ME2 gives you war assets and changes the game in certain situations, but this is kind of a stretch.