Both of these verbs are used for asking about something or looking for information. The nouns for the request / investigation are enquiry and inquiry.
Technically, enquire is used for "ask" in general ("He enquired about prices for the products"), and inquire for a more formal investigation ("The police will make an inquiry into the alleged corruption.")
However, in American English it is now very common to use inquire for everything: "He inquired about prices for the products."
The Gashouse Gang was a nickname applied to the St. Louis Cardinals Major League Baseball team of 1934. The team won 95 games, the National League pennant, and the 1934 World Series in seven games over the Detroit Tigers.