The most runs scored by a winning team in a MLB game is 30.
The most runs the Mets have scored in one game is 23 in a game against the Cubs on August 16, 1987.
The most runs scored in an inning by both teams is 19 in the 8th inning of a game between Cleveland and Boston in 1977. Cleveland scored 13 runs and Boston scored 6. The most runs scored by a single team in aninning is 18 by Chicago against Detroit in the 7th inning of a game played in 1883.
11 home runs ***During a "series" not a game. I know the Giants had 14 one year....
42 to 5
Edgardo Alfonzo scored 6 runs at Houston on August 30, 1999. Alfonzo also set club records for most hits in a game (6), most home runs (3 (with 7 others)), and most total bases (16 (3 HR, 2B, 2 1B))