I just wached the Rays hit 5 solo homers all by themselves and all against CC Sabathia to beat the Yankees. So I say 5 HR by a single team in a 9 inning game.
There is a reason why they say the Big Ten Conference is the most difficult conference in NCAA, but there were 8 teams total. Nebraska, Michigan, Michigan State, Iowa, Ohio State, Northwestern,...
According to this website: http://www.baseball-almanac.com/recbooks/rb_runs2.shtml which seems to be pretty accurate, the answer is 49 runs for the NL and 36 runs for the AL