Hi Taner
Thomas is correct in that 'left' and 'right' are kind of arbitrary terms relative to the view of the user - better to think in terms similar to boats where 'port' and 'starboard' relate to the object. Which for lines, the direction it was drawn determines this.
The following might be one way to check, note I haven't tested.
Use the nearestCoordinate method of your line geometry with your point as input. Get the distance from the original point to this new calculated point. Draw two new lines offset either side of your line by that distance. Check to see which line intersects the original point and that will tell you which side the point is offset by.
Might not be the most elegant solution but should work if no one else has any other suggestions...
Cheers,
-Paul