oxforddictionaries.com has this as the first definition of tap (n):
A device by which a flow of liquid or gas from a pipe or container can be controlled.
and for the verb,
Draw liquid through the tap or spout of (a cask, barrel, or other container)
When you tap a barrel of beer, you can get the beer out of it.
When you tap a certain kind of maple tree, you can get fluid out of it that can be used to make maple syrup.
The usage you refer to is based on this literal meaning of tap.
Prepositions don't have to be part of a phrasal verb, in fact I would say most aren't. In this case, none of the prepositions have any special relation to the verb. They're all literal descriptors of the positions the subject goes through during the action.
Try to break up the sentence into the smallest chunks that make sense. Here: He fell. Yeah, that makes sense, that's true. Okay, where did he fall? Into the pool. What did he fall off of? He fell off the ledge. So now, put it together.
He fell off the ledge and into the pool.
You can leave out the "and" here, but it's still there for grammatical purposes. You can tell if you use three prepositions:
He fell off the ledge, through the air, and into the pool.
You can't leave out the "and" here, there's no way to use three prepositions without the conjunction. That means that there's no way to do it with two, either, and the "and" is still there, it's just not spoken.
Right and straight are both intensifiers, and don't really make sense to me here. There's not exactly an indirect way to fall off a ledge and into a pool.
I hope this helps.
Edit: A note to help distinguish between phrasal verbs and normal prepositional adverb phrases: phrasal verbs don't accept objects of the preposition, and they don't pair with prepositions in conjunction phrases.
The roof fell in. good
The roof fell in the house. not good
The roof fell in and onto the ground. not good
The roof fell in onto the ground. good
Does that help you see the difference a little better?
Best Answer
Intuitively, I feel like the addition of "over" implies that the destination is a house. I can think of a few phrases that fit this description:
I can't think of an example where you would use one of these without implying that the destination is a house. For example, you wouldn't really say "I'm at work, do you want to come over and pick me up?" Or, "I brought all my books over to school."
I know this isn't a very scientific answer and some will disagree, but as a native speaker I feel like that's the shade of meaning that "over" gives in this case.