According to College Football Data Warehouse, The Georgia Bulldogs are 18-21-2 alltime against the Tennessee Volunteers.
21-15-2
Georgia Tech is 17-24-2 all time against Tennessee. The last game between the two schools was in 1987.
Through the 2009 season, Tennessee leads the all time series against Georgia 21-16-2.
Tennessee 21, Georgia 16, 2 ties (as of end of 2009 season) As far as I know, there are no disputed games in this series (as opposed to, for example, the Georgia-Georgia Tech series), so the record should be the same no matter which side you ask.
25-36-4
Tennessee has 72 wins to 28 losses against Vanderbilt they also have 5 ties.
Through the 2008 season, Pitt's all time record against the SEC is 8-1-2. All of the games Pitt played against SEC teams (Florida, Georgia, South Carolina, and Tennessee) occurred between 1973-1985.
After the October 11, 2008 game between Georgia and Tennessee, since 1999 Georgia has won six times (2000, 2001, 2002, 2003, 2005, 2008) and Tennessee has won four times (1999, 2004, 2006, 2007).
Tenesse currently trails the series record 19 to 20.
Alabama leads the series against Georgia 35-25-4 in 64 meetings as of the 2009 season.
In Tennessee their Monday Night record is 8-5.
Through the 2008 season, Tennessee leads the all time series against Memphis 20-1.
Through the 2011 season, West Virginia and Tennessee have not met in a football game.