How to deal with the swarm?

I'm playing Dead Space demo for the Xbox 360 and this thing is sick. And when I say sick I mean, dissolving-puppies-with-acid-and-feeding-poor-children-with-the-resulting-paste sick.

Anyhow, I'm using some weapon that cut the things into little pieces, but the little pieces jump at my neck and kill me, I shake them once but they attack me again.

What is the best strategy to kill these horrid undead meats?

If you're talking about the Swarm:

Swarm: Swarms are the creatures that come from a Pregnant who has been shot in the belly, and sometimes are found in independent swarms or inside item crates. They are extremely weak, but tend to swarm en-masse and do a lot of damage to Isaac by attaching themselves to his body. However, their weakness and the density of their swarms can be cleverly used against them. They appear as a small lump of green flesh with small tentacles, and move by rolling with their appendages. They can leap great distances.

(source: http://strategywiki.org/wiki/Dead_Space/Enemies )

then I would heartily recommend the force gun. One shot and they are all toast. On the higher difficulties where you don't want to waste any ammo at all, use stasis and then stomp the little buggers.

An ounce of prevention is worth a pound of cure. When you kill the initial creature (Pregnants) avoid shooting it in the stomach and instead go for the limbs or head. Then you won't have to deal with the critters at all.

If the parent creature is a "Divider" then I don't think this strategy works.

If they do get out, the flamethrower and ripper are also pretty effective.

You should move back while firing at them, always keep them all in front of you, and do not let them flank you. But this I can say about almost every monster in the game.

Best weapon choice is something with large clip size and fire rate — pulse rifle, plasma cutter (if you have upgraded its clip size). Flamethrower is perfect, but it is rarely kept in the inventory because it is ineffective against other enemies.