I'm looking for the name of a story (as well as the author and issue,
if possible) of a story which appeared in "Highlights" magazine years
ago when I was a kid.

It concerned a family who had a travelling aunt. Every so often, she
would send the family some new, exotic gift. One of these gifts was a
seashell, which, when it was put to the ear, would whisper a nonsense
phrase. Unfortunately, this phrase became all the person could say.
One of the kids listened to the shell and ended up saying,
"Shisk-a-bob-a-bob-bob"; the father ended up saying
"yora-gora-stink-blink". At the end, the toddler of the house found
the words to end it all on a piece of paper in the bottom of the
shell's box: "Jiggla sniggla breaks the spell".

Hope I've been detailed enough. :)

It might help if we knew approximately how long ago you were a kid.
Are we looking for a story published in the 1950s? 1990s? Finding the
story may be a long shot, but narrowing down the time frame could be
helpful.

Sorry about that, I typed this question before bed! It should be late
80's-early 90's.

This website has an index to all highlights articles back to 1986.  

http://www.highlightskids.com/OLIndex/h8guestKidsIndex.asp

I've been unable to find the article in question but perhaps you or a
researcher may have luck.

Could this be it?

Listening Shell, The by Donnaleen Howitt 
October, 1989,  Page #: 22
Category: Stories (fiction)--More advanced reading
Daniel is lonely on his island until he finds an amazing shell.

No, but thanks for the site ... I FOUND IT! 

Jiggla-Sniggla by Janet S. Anderson 
March, 1992,  Page #: 36
Category: Stories (fiction)--More advanced reading
Aunt Tessie's annual presents were "different," to say the least.

Yay me!