The super over is treated like penalty shootouts in football. The goals scored during the shootout is not added to the players career goal tally. Similarly, the efforts of cricketers in the super over is not added to their career stats.
Batting averages are calculated on the basis of (runs scored / (innings - no. of not-outs)).
Bowling averages are calculated on the basis of (runs scored off bowling / wickets taken).
Here the runs and wickets are what the players score or take in the match prior to the commencement of the super over.
EDIT: Chris Gayle was on 4999 career T20 runs before the start of the RCB v DD game on 16-Apr-2013. The first ball he scored a single to move to 5000 runs. He ended up scoring 13 in that innings and 2 more in the super over. However, ESPNcricinfo (forgive me for my photoshopping "skills") has his career runs as 5012 (4999+13) and not 5014, meaning it only considers the runs scored in the main match and not the super over.