ReadySetUnsheathe has a series of instructions on how to sword fight medieval style.
complete with medieval illustrations.
Galdalf's sword is a traditional longsword.
however, Thorin Oakenshield's sword is actually a dao,
a one side sharp weapon related to the much beloved Philippine Bolo....
photo From wikipedia commons.
if it resembles a "long sword" rather than the shorter dao, it might be because it is being used by a dwarf, and not a taller elven lord. And Arwen carries one in the FOTR
Heirs of Durin discuss the weapon here.
Instructions on how to chop can be found HERE
I can't find much on Sting, on the LOTR pages, but since it had "blessings" on it that enabled it to cut spider webs, it might have been used for this during the wars of the first age: a shorter dagger would be easier to use than a longer sword. But that doesn't explain why it is a two edged sword.
SwordDigest however has a nice long discussion of the STING survival knife similar "commando" knives HERE. These knives are shorter than Bilbo's blade (even when one considers Bilbo is only 3 foot tall and dwarves tend to be over 6 feet), but the comments on why they are double edged and useful in close combat may give you an idea why it might have been used in the first age.
and Wikipedia adds this piece of trivia: