Teleportation does not require Line of Effect, but Line of Sight is still necessary. In your example, the Eladrin would only be able to teleport to the previous room if the wall he was backed up against had a window.

Other notable differences from normal movement are:

• Does not provoke opportunity actions.
• Unhindered by objects or terrain in the path of travel.
• You must be able to occupy the target space without squeezing.
• Can be done while immobilized or restrained, and negates these effects if you are teleporting out of the affected area.

Here's the (nearly) full Compendium entry, which covers these items and more:

• Instantaneous: Teleportation is instantaneous. The target disappears and immediately appears in the destination space you choose. The movement is unhindered by intervening creatures, objects, or terrain.

• Destination Space: The destination of the teleportation must be an unoccupied space that the target can occupy without squeezing. If arriving in the destination space would cause the target to fall or if that space is hindering terrain, the target can make a saving throw. On a save, the teleportation is negated.

• Line of Sight: You must have line of sight to the destination space.

• No Line of Effect: Neither you nor the target needs line of effect to the destination space.

• No Opportunity Actions: The target doesn’t provoke opportunity actions for leaving its starting position.

• Immobilized or Restrained: Being immobilized or restrained doesn’t prevent a target from teleporting. If a target teleports away from a physical restraint, a monster’s grasp, or some other immobilizing effect that is located in a specific space, the target is no longer immobilized or restrained. Otherwise, the target teleports but is still immobilized or restrained when it reaches the destination space.

Teleportation does not require Line of Effect, but Line of Sight is still necessary. In your example, the Eladrin would only be able to teleport to the previous room if the wall he was backed up against had a window.

Other notable differences from normal movement are:

• Does not provoke opportunity actions.
• Unhindered by objects or terrain in the path of travel.
• You must be able to occupy the target space without squeezing.
• Can be done while immobilized or restrained, and negates these effects if you are teleporting out of the affected area.
• Can be done while prone, though it does not negate this effect.
• Unless otherwise specified, does not move a Mount and its Rider together. (Rider falls, if dismounted.)
• Teleportation speed is not affected by the Slowed condition.

The Compendium entries on "Teleportation", "Mount and Rider", "Slowed", and "Prone" cover all these points and more. The same information is also available in the Player's Handbooks.