Why do sound waves need a medium?
Because they're mechanical waves.
Sound wave is a progressive wave that'll transfer energy between two points.
In order to do that, particles on the wave, will vibrate to and fro, collide with each other and pass the energy. (Keep in mind that the particles themselves do not change overall position, they just pass the energy by vibrating.)
This happens in a series of compressions (areas of high pressure than normal, where particles are closer together) and rarefactions (areas of lower pressure than normal, where particles are more spread apart).
So, there must be particles vibrating in the direction of the wave's velocity and colliding with nearby particles to transmit the energy.
That's why sound travels fastest in solid. Because the particles are closest together and energy will be passed on fastest.