Long story short, I need to kill a teammate, but unfortunately, our scouts include an elf and a shardmind. I read that eladrin instead of sleeping during their extended rest, enter a trance, but there are conflicting theories about whether that applies to elves as well. If the elf actually sleeps, it would make my job much easier. Do they sleep?
So um, aside from strongly advising you not to engage in PVP within the DnD4e ruleset (which is incredibly bad at PVP), and more generally to not murder your teammates, I'm happy to answer your rules questions.
You seem to have more than one question rolled in there, so I'll address them one at a time.
How aware are eladrin while trancing?
The rules text for eladrin says, "While in a trance, you are fully aware of your surroundings and notice approaching enemies and other events as normal"
Are eladrin immune to sleep effects, since they don't naturally need to sleep?
No. In 4e, this immunity was replaced by a +5 to saving throws against charm effects.
Do elves trance or sleep?
There is no reference to trancing in the rules for elves, so they sleep. I have no idea who is telling you that there's "conflicting theories" about this, but there aren't. Elves aren't eladrin, and one of the differences is that they sleep.
Are shardminds immune to sleep effects, since they don't naturally need to sleep?
There is no reference to immunity to sleep effects in the rules for shardminds, so they are not immune to sleep effects.
Do attacks that render a target unconscious stack with natural sleep?
What is the effect of stacking magical Sleep with natural sleep?
When two effects caused by different named rule elements are causing the same status effect on a creature, they stack so long as their durations are different. (i.e. A creature can be both dazed until the end of their next turn AND dazed save ends, but cannot be dazed save ends twice)
Ordinarily, creatures hit with an effect are automatically aware of all of the effects of that effect unless the attack specifically says that the target is unaware it was affected. So if you cast (or poison) Sleep on a target, it knows that it is being magically rendered unconscious. It is up to your GM to determine whether this still applies to creatures who were already unconscious, but it would certainly apply to the Shardmind.