I just tried playing in offline mode, and it states that you cannot use power-ups or post scores to the leaderboard in this mode.
For the track power-ups, there are six different ones that can be unlocked. The first is Synchrony, where you earn points for switching tracks on measure markers. The other five are basically just a variation on the same concept. The Super Guitar makes guitar notes worth more points. Then there's Super Bass, Super Drums, etc.