"If there is no sound in space, then when something happens that would have made a sound in the presence of air, do the sound waves travel at all in vacuum?"

In Earth sea level atmosphere there is 1 X 10^14 molecules per cubic cm [10 trillion molecules per cubic cm].
On the moon there is 4 X 10^5 per cubic cm
In interplanetary space there is 10 molecules per cm3

So, earth's atmosphere is sort of like a ocean of air- hit something, and it vibrates and sends waves and these waves causes ear drums to move and send signals to the brain and brain "makes" sound.
Same thing can occur in space, but there is less molecules so sound doesn't "carry" over distance. In real ocean or lake, sound carries further than in air- because water is denser than air, so with less dense atmospheres sound doesn't travel as far.
The other part is the ear hearing the sound. Put on full motorcycle helmet and you could get some idea of the problem with hearing. In a space helmet- at sea level atmosphere- you going have hard time hearing sounds, unless it's miked into the helmet.
Mars has 1/100th of Earth's atmosphere [somewhere around 100 billion molecules per cm3]. You can't expose your ears in a Mars atmosphere, but you can use a microphone. On Mars you could play recorded music using typical sound system. The music probably would sound different and you will need to crank the sound up higher to hear it [via a microphone].
On the moon this wouldn't work. Though speakers that could cause your ears to bleed, might make a sound which detectable at a short distance.

"If they do and eventually come to a planet with air, would the sound then be heard?"

No.
Any sound in space would deaden very rapidly in a denser atmosphere. Think of trying to hear someone talking to you if you are under water.

To hear the noise of the sun, you would need to be in the vacuum of space. And if you had a microphone which mimicked the hearing capability of a human ear, I'm not sure you could hear the sound, and this, the largest sound maker in this solar system.