Why do sound waves travel faster in water than light waves? If light waves travel faster than sound waves in the air, 
why do they travel slower than sound waves in water?
Is there any difference in how light and sound waves refract when they enter the water? 
 A: In a sense, the question is a little confused, because light waves travel faster than sound waves even in water.
So, I guess what you want to ask is: the light waves travel slower in water than travel in air, but the sound waves travel faster in water than travel in air, what makes the different tendency?
I think the reason maybe light and sound are different in essence.
light wave is transverse wave, sound wave is longitudinal wave.
light is electromagnetic wave, it produced by the electron transition,  electromagnetic wave is the transmit of energy, it travels don't rely on medium. The exsit of medium will then reduce the travel of light, the water reduce stronger than air.
Sound is produced by the vibration of matter, it travels by the matter interact with each other. So it depend on the medium, the density of water are larger than air, then the interaction between the water molecule are larger than air molecule. It leads to the speed of sound waves in water are larger than in air.
A: Light travels faster than sound even in water. If you are asking why sound is slower when it is in air than water, and why light is faster in air than in water, here is why:
Light waves are electromagnetic transversal waves. They can travel through a vacuum and any particles they contact slow them down. So when they move through denser water they are slowed down more.
Sound waves are compressional waves that occur by particles hitting each other and moving the vibration along. Water molecules are more tightly compacted together so the vibrations can travel more easily than through air.
A: 
If light waves travel faster than sound waves in the air, why do they
  travel slower than sound waves in water?

They don't.
Google "speed of sound in water" = 1498 meters per second
Google "speed of light in water" = 225,000 kilometers per second
The second is much larger than the first. :-)
