Based strictly on definitions from average dictionaries it's probably hard to find anything technically wrong with any of the three; however, I never hear native speakers use the first sentence and native speakers will invariably say you can get to street 'B' from street 'C'. The other two sentences are native-sounding (although probably more common is going down or even going up rather than going on but all are expressions I've heard from native speakers).
I believe the reason that you can get to street 'B' by street 'C' is somewhere in the range of incorrect to much less preferable than you can get to street 'B' from street 'C' relates to advanced theories of language and culture which are beyond the scope of most dictionaries.
The book The Way We Think: Conceptual Blending And The Mind's Hidden Complexities by Gilles Fauconnier and Mark Turner makes a relevant examination of theories of language developed by Len Talmy, especially Talmy's theory of Access Path expressions:
[Human beings] have a standard way of using conceptual blends to give
insight into location, shape and contiguity....As Talmy writes, "Most
observers can agree that languages systematically and extensively
refer to stationary circumstances with forms and constructions whose
basic reference is to motion."....we have the overachieving goal of
achieving human scale, and the scene. It is more congenial for human
beings to process a full, dynamic, intentional human scale action than
it is to process one apparently simple component of it."
The book then gives several examples such as: The mountain range goes all the way from Mexico to Canada and The field spreads out in all directions from the granary and the more subtle The bakery is across the street from the bank.
This last example you will notice is very similar to your first sentence. The book explains:
The static input could be expressed by "The bakery is on the street."
The motion input has something departing from one point, traversing
some surface, and arriving at another point. The words "across" and
"from" come from the motion input....In the bakery example, the motion
input has a surface that is traversed. Its counterpart in the static
input is the street. In the blend [ie both "across" and "from" which
create a fused element], the surface traversed is fused with the
street; we can use the label "the street" to pick out that fused
element in the blend and the put "the street" in the grammatical
position for the surface traversed ("across the street").
So, from is a word that creates a motion input. If you say you can get to street 'B' from street 'C' you have a static input (street 'C') and the motion input from, creating the Access Path expression which is normal to languages (not only English but most if not all languages according to Talmy). However using the word by is not a motion input (which is why native speakers who use by add additional words that creates the motion input such as your other sentences by taking or by going down/up/on), so using by would create language with only a static input which is only a component of the human scale action and returning to Talmy's theory quoted above:
"It is more congenial for human beings to process a full, dynamic,
intentional human scale action than it is to process one apparently
simple component of it."
EDIT: another answer claimed that you can get to street 'B' by street 'C' clearly implies the unsaid words you can get to street 'B' by [taking] street 'C' which is completely incorrect. To begin with, why not the unsaid words you can get to street 'B' by [going down] street 'C'? In a comment below, @fixer1234 said that he thought that if there were implied words they would be you can get to street 'B' by [way of] street 'C', another option. And if there's no clarity on what the supposed unsaid words are then we can't say they exist - you cannot use unsaid words which are not clear. But even more relevant, there's a perfectly acceptable definition that would allow a speaker to use by without any additional implied words:
- over the surface of, through the medium of, along, or using as a route:
He came by the highway. She arrived by air.
So it cannot be conclusively said that there must be additional implied words and, as I mentioned above, based on a simple reading of the dictionary, one might conclude that the first sentence is fine. It's only when we consider more advanced theories of language like I presented that it becomes clear why native speakers don't tend to use the first sentence.
I'll add to my edit that this same answer claimed that going through a street is the preferred expression but I'll stick by what I said above that most native speakers would say going down the street and the next most common would be going up the street and only after these do we start to hear expressions like going on the street or going through the street.