Space is comprised pretty much of the entire area outside of the Earth’s atmosphere, and much of it is relatively empty, so it could be understood by many that it has no odor of its own. It may be true that the rareness of the particulate matter in space would make it less likely for people to be able to put their head out of their space station or ship and breathe in an aroma, but space does have its own smell.
Taking a quick sniff of the local solar system is a good way to begin, but it should be kept in mind that it is dangerous to go outside to space without a full spacesuit. For those wishing to know the local odors, it can be as simple as smelling the residential odor on the outside of the suit. Those relatively rare particles found in space tend to glom onto whatever they pass, and a spacesuit is just as good as a planet, space station or even a passing asteroid.
Scientists have analyzed the particles that come back attached to space suits, but astronauts were the first to describe the odors. Many of them say the smell of cooked steak accompanied them back into their vehicles, and the scientists have confirmed this. Burnt carbons from stars are responsible, and less oxygen available for the burning makes it more pungent. Thus, the steak or burning smell is generally what local astronauts in Earth orbit will get when they come back inside.
There are other airless places man has already reached, and the moon immediately comes to mind. Astronauts who have landed there reported their suits smelled like gunpowder. It does not mean the moon is primed and ready to shoot, but it does mean there are different ingredients that have stuck to spacesuits. In this case there would still be carbon, but a sulfuric element would also need to be present to create just the right aroma of a freshly fired gun.
Steaks and gun powder might be the most obvious local aromas, but different atoms cruising through the solar system could change the smells slightly. Every star burning brightly in the night sky throws off particles that will continue to float until they hit another star, a planet, or even an astronaut, and it is likely that they might eventually reach a spacesuit being brought inside. These aromas have been theorized to smell mostly like burning hydrocarbons that come from charcoal grills or diesel engines.
No one can categorize every smell of the space between the stars right now, but scientists are working hard to isolate all the different particles that are likely to float in eventually. Different combinations might create a range of aromas, but only time and sniffing will tell.