The name refers to MD 20/20 (aka Mad Dog 20/20) and Night Train Express, two brands of wine known for their low price and low quality.
The When Consumed message may refer to a type of wine known called port wine.
The expression "any port in a storm" alludes to the fact that a ship can't be choosy as to where it berths when it desperately needs shelter. Thus "If you need to get drunk, this stuff might be lousy but it'll do the job."