The performances aren't just for kids. The trio has spent countless hours doing free performances at hospitals, nursing homes, churches, schools and camps, as well as for many other organizations.
McVeagh has been teaching magic since 1972, and he gives classes through Washington County Parks and Recreation Department.
Greer and Burkett were two of his students. Burkett never had performed magic before he took McVeagh's class in 1987. Greer started doing card magic when he was in college, and he took the class in 1992.
McVeagh, 69, who became interested in magic when he was about 15, has been giving shows at National Institutes of Health in Bethesda, Md., since 1970.
He asked Greer and Burkett to do a charity show with him, and that set the stage for their association.
"They were so good; I asked if they'd mind doing it, and it went from there," McVeagh says.
They tailor their magic to the ages of the people in their audiences. All three do stage magic, comedy and audience participation, as well as walk-around or close-up magic, such as card and coin tricks.
Balloons are transformed into animals by a few twists of Greer's deft fingers. Hortense the ladybug helps Burkett with card tricks, and Cornelius the crow puppet adds commentary to McVeagh's routine.
"I'm not that good of a ventriloquist," McVeagh says, glancing at Cornelius.
"He's a terrible ventriloquist," Burkett pipes up with a smile.
The good-natured banter flows fast and freely among the three members of King Ring 94, the local chapter of International Brotherhood of Magicians.
Besides doing charity shows, each operates his own magic business. Greer bills himself as Jim the Plain-Clothes Clown, Burkett is known as The Dean of Magic, and McVeagh calls his business Magic by McVeagh.
McVeagh, of Hagerstown, retired from the Nuclear Regulatory Commission in 1984 and works part time at Blaine Window Hardware Inc.
Burkett, 60, retired from the U.S. Department of Defense in 1993, and he and his wife, Brenda, live in Williamsport.
Greer, 43, a Hagerstown resident, is single and works for the Maryland Department of Agriculture.
About 50 of the 200 shows Burkett does each year are on a volunteer basis. Most of the 50 performances given annually by McVeagh are for charity, as are about half of Greer's 75 to 100 shows.
Each usually does a separate routine, telling stories as he performs. Greer knows sign language and uses it if needed.
Performances for terminally ill children are especially moving, McVeagh says, adding that at times he's been overcome with emotion and has had to walk offstage.
"These kids are remarkable. They're laughing and carrying on, and they're dying," he says.
Burkett says they strive to make children who are sick feel special and to let them participate.
"We make stars out of these kids," Burkett says.
Before they do a stage show at a hospital, they go through the rooms to do some tricks for patients too ill to get out of bed.
"Just getting a smile out of a kid in a hospital room is pretty important," Greer says.
Some in the audiences don't speak English, but the language barrier is overcome because magic is universal.
"We try to gear it so everyone has a big belly laugh," McVeagh says.
McVeagh says he finds the work very spiritual.
"I used to come home from NIH and wake my son up and just hug him," he says.