What was so funny about the telegrams?
The telegrams are actually short letters from guests who could not make it to the wedding, sending their wishes to the newlyweds.
SHERLOCK: First things first. Telegrams.
(He picks them up and shows them to the guests.)
SHERLOCK (quick-fire): Well, they’re not actually telegrams. We just call them telegrams. I don’t know why. Wedding tradition.
(Same transkript, next scene)
It is the best man's job to read them at the wedding.
It was my understanding that Mrs. Hudson was thinking about how Sherlock would have to read all those emotional letters, filled with words of endearment, out aloud, and the thought amused her.
He is a very rational character and has little empathy for such kind words, so he is probably the worst man for the job. In fact, he ends up skipping most of them because he simply finds them unnecessary and irritating:
SHERLOCK (reading the next card): “To John and Mary. All good wishes for your special day. With love and many big ... (he breaks off, then continues slowly) ... big squishy cuddles, from Stella and Ted.”
(He looks up, blinking rapidly. Greg sniggers and Molly smiles.)
SHERLOCK (reading the next card): “Mary – lots of love, ...”
(He breathes out an almost silent, ‘Oh’. John and Mary look up at him.)
SHERLOCK (disparagingly): “... poppet ...”
(He loudly sounds the ‘t’ at the end of the word. John and Mary giggle.)
SHERLOCK: “... Oodles of love and heaps of good wishes from CAM.”
Then, after a moment he loses all hint of patience.
SHERLOCK (looking at the next card): Um, “special day” ... (he drops the card onto the table and looks at the next one) ... “very special day” ... (he drops that one, then continues working rapidly through the next ones) ... “love” ... “love” ... “love” ... “love” ... “lo...”; bit of a theme – you get the gist. People are basically fond.
(There’s some laughter from the guests.)
The guests end up finding this funny, mostly because they know how uncomfortable this is for Sherlock. This was probably also what Mrs. Hudson was anticipating and what was making her laugh.