One of the quests in Evendim, on the island infested with salamanders, is about killing insects on the island. Why? The Ranger there thinks he saw one of them carry a salamander on its back while swimming(without a loss to mobility, as well!), and fears that if kept unchecked, the salamanders would be able to reach the mainland this way. However, the quest journal states that you fail to see how the insects would be able to carry the salamanders, the Ranger states mid-quest that he may have been imagining things, and when you do finish it, he admits that there is no way that it was actually possible, but thanks you for doing it anyway. The Ranger was on the island for a long time with the self proclaimed "Greatest Lore-master Ever", who caused all of the salamanders to appear, and acted insane until the end of his quest series.
Another quest in Evendim involves drugging a giant's soup, causing several giants to hallucinate, resulting in several hilarious reactions.
In the Trollshaws, one quest chain revolves around collecting ingredients for a toad soup recipe, making an "improved" version of the soup to the dwarf who gave the questgiver the recipe, and then giving the soup back to the questgiver, only for him to be tricked by the dwarf again. The chain ends with this line, after he says that he'll find a reward for you:
"No, no, do not look so panicked! I was not planning on giving you the toad stew!"
From the description of a quest reward from a Trollshaws quest chain:
"Wistan wishes you to spread the tale of how he isn't skilled enough to catch a cradle-robbing creature. How odd."
From the description of a pair of special shrew-stomping boots, from the elves' Spring Festival:
"These boots were made for stomping, and that's just what they'll do. One of these days, these boots are going to stomp all over shrews."
In Angmar, down in Ram Duath, there's groups of orcs that are occasionally led by a captain, who keeps yelling some damn hilarious things at them. (Especially when you realize he's congratulating himself for not killing off his moronic subordinates.)
“Yes! Me good leader! Still got three Orcs left to push war-wagon!”
“Stop. We rest now. Not kill off last few Orcs.”
“Should kill you now. But then, who push wagon?”
During Epic Volume III, a Dunlending Man named Iwan has you gather toxic toad-residue for him to treat his clan's weapons with. Upon bringing him the residue, he immediately taste-tests it. He becomes quite ill, but is pleased at how effective the poison is.
Maelona: "Iwan is a fool and always has been! Never taste the poison you are making! *sigh*"
Iwan: "I feel...terrible...is that not wonderful?"
A quest in Lothlórien requires you to scold drunken Elven revelers without disturbing the sober ones. The way to determine who's drunk? They butcher their repeated dialogue with hilarious malapropisms!
Reveller (sober): 'Aesbrennil's berry-pies make a wonderful end to the meal!'
Reveller (drunk): 'Aesbrennil's buried pies make a splendourful end to the maul!'
At the end of the Moria- and Mirkwood-storyline, in an optional quest as part of the epilogue, a dwarf tasks the player with killing an orc or a goblin in every region of Middle-earth (prior to Mirkwood) in his family's name, after which you are to tell the dwarf's father of your glorious exploits. The father is less than amused, bemoaning the fact that his sons spend more time complaining to strangers about their grievances with the orcs, than actually doing something productive. He also questions whether or not the player character hasn't got anything more important to do.
Tandri (the father): 'What in the names of all the Fathers has my son had you do?'