If vast areas of outer space contain nothing, does that mean those areas contains no atoms either

The "vacuum of space" refers to the relative lack of material in space.

The Earth's atmosphere doesn't really stop at a certain place and then "space" begins. The air gets thinner as you go up from the surface and the farther from Earth (or the Sun) you get the thinner it is. It gets thinner still if you leave our solar system and even thinner in intergalactic space. But it is always there.

In reality, no volume of space can ever be perfectly empty. A perfect vacuum with a gaseous pressure of absolute zero is a philosophical concept that does not exist in nature.
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"Nothing" of course means just that...no molecules, no atoms. As Nyx correctly pointed out, there's always various kinds of energy present everywhere, but since you specifically asked about atoms it has been estimated that "empty" space contains on average something like 1 to 2 hydrogen atoms per cubic meter.

ADDENDUM:
Almost forgot about so-called "dark matter," but of course we still don't know what that is, but whatever it is makes up about 23% of the universe and has characteristics like regular atom-based matter.

If anything, you have energy passing through like photons, radio waves, and the odd occasional atom or two. Then you have high energy radiation like gamma and x-rays whizzing by. Then there are the neutrinos, by the billions, but they are snobbish and don't interact with hardly anyone.

No, it can't be said that vast areas of space are empty, because only a tiniest fraction of space has been discovered. Moreover, there would be atoms or any other particles of atoms such as free neutrons, protons etc. I hope my message is clear to you.........

No. Even though space is far emptier than the hardest vacuum we can make on Earth, there are still atoms to be found everywhere, just not very many of them.