PART ONE (see my other comment for part 2)
They can be used interchangeably in some scenarios, but not others. They can also be combined.
"As soon as" is talking about the order of tasks. Usually you are saying you will do one thing directly after another, or that something happened directly after something else.
"I will go to sleep as soon as I finish this movie" = First the movie ends, then I will go to sleep
"I will never play chess with him again because he's a cheater! As soon as I looked away, he moved the pieces." = First I looked away, then he moved the pieces
"Just as" can be a comparison between two things, implying they are <em>equals. </em>
"Oranges are just as tasty as apples!" = oranges and apples are equally tasty
"You say he is mean, but you are just as rude as him." = the two people are equally rude
In these instances, you could only use "just as". They would not make sense with "as soon as" since you are not talking about time or the order of tasks.
That being said, "just" can be added to "as soon as", to make "just as soon as". Although it is not a perfect translation, just means equal, and it helps to think of "just" like you would think of "exactly".
"Oranges are exactly as tasty as apples!" = the meaning hasn't changed. The sentence is still comparing the fruits, and judging them to be equal.
Or, "I will go to sleep exactly when this movie ends." = the meaning hasn't changed. The sentence is still about the order of tasks.
"Just as soon as" is only emphasizing that you will do second task RIGHT AWAY after the first task.
I didn't have room to finish: This is PART ONE of my answer