They are all generally the same. Depending on what you want to say, some will be used in one context but not the other. For example, you will hear "wash away" in regards to something other than ourselves doing the washing. For instance, the ocean will wash away your sand castle, or wash away footprints on the sand. Wash out and wash off are active verbs in that someone such as yourself is doing the washing. Wash away will also be found in songs and poetry often. Like Soundgarden's "Black hole sun, won't you come and wash away the rain?" "Wash away the pain," like this. Wash off is more common than wash out. If you use wash out, you will usually put the noun in the middle. Like "I need to wash the bucket out." But you could also say "I need to wash out this bucket." You wash out something that has an insides. Usually. People used to commonly say they needed to "wash out" their hair, but this is not as common except maybe in hair salons. They will also say "blow out" (for blow dry and style hair) which I think is adapted from the idea of "wash out." Wash off would be most commonly used when people are dirty. "I need to wash off the grime." "Let me wash off this paint."