Is it possible to change default EventKitUI style? I'd like to have different background (transparent), also black translucent navigation bar and buttons.
Maybe there is a way to override default style for the whole app?
No. That is all controlled by apple. You can change a few colors here and there. Look at the documentation for UINavigationBar or whichever component you want to work with. Some things have a color or style setting others like UIAlertView's do not.