How old were George and Fred when they opened the shop? I've been looking for the answer but it only shows what year they dropped out of school.
The HP Lexicon places the date of the shop's opening as April 16th, 1996, reasoning
... since the chapter before Fred and George leave Hogwarts took place on a Monday in April, the chapter in which they leave must take place Tuesday and Wednesday of the same week. Hermione also says that the Easter holiday begins Friday...
Assuming this is accurate (and knowing that Fred & George were born on April 1, 1978), then they would have been 18 years and 15(?) days old when they opened the store, even taking into account that we don't know the precise date of the Easter holiday.
That being said, the company was most certainly already set up before they left Hogwarts, so Wizard Wheezes (the store) may have been owned and operated prior to their 18th birthdays.