"Is L2 truly empty? Has anyone checked recently? How about the other L points?"

It's a good question. Depends on the resolution at that distance and whether anyone has looked.*

Another thing to keep in mind is that what is called Earth/Sun L-2 is a vast area and a small portion of it is in the Earth's shadow {since the earth's shadow can block the entire Moon [though L-2 is much further from the Earth than the Moon] the area constantly blocked by the earth is somewhere around size the Moon. And in terms of 3 D, the volume of this dark area should be much more than the volume of Moon}.
I would imagine that if a rock say smaller than the size of house was in L-2 it wouldn't have been seen, nor could it be possible to see it. A large radio telescope probably wouldn't have enough resolution to see such a small object at such a long distance- though I imagine if painted with strong enough radar signal that could be a different matter.

*Earth/sun L-2 is about 1.5 million kilometer from Earth. But reading some sources on internet, it seems to say seems that it's too far to have the Earth block the sunlight.

But at http://en.wikipedia.org/wiki/Lunar_eclipse
Regarding Lunar eclipse it shows that the Moon can fit easily within the Earth shadow [about 2 1/2 times the moon diameter for total eclipse (in the umbra part) and including penumbral it's about 4 1/2 times. Since 1.5 milion km is slightly less than 4 times the distance to the moon, therefore at 4 times the distance of the Moon the Earth's shadow including it's penumbral should be slightly larger than the Moon and it's umbra part should be slightly over 1/2 of the Moon's diameter. Also in my wandering it mentioned that the telescope going to in L-2 should visable by amateur telescopes, I find this hard to believe. It would similar [but obviously not the same] to say that amateur telescopes can see the apollo landing sites.