I think they all mean roughly the same thing – if you told me one of these statements, I'd expect your address to be something like 1427 Downing Street (or someplace near that) – but there might be some contextual differences in when you would say them.
First off, I don't think any of the four would be my choice of preposition if someone asked me where I live. Instead, I'd usually say:
I live on Downing Street.
or, if I was giving the exact address:
I live at 1427 Downing Street.
However, some of the prepositions you mention are often given when people provide directions. Consider the map below:
Let's also assume Pace St. is a fairly well-known location – if you and I were in a conversation, we'd both probably know where that road is, and how to get to it. With that in mind, here are some questions you might ask, and how I might answer them:
Where do your kids go to school?
At the Goddard School.
Oh, where's that?
The Goddard School is off of Pace Street.
Actually, the school is on Olympia Ave, but I'm guessing that, if you knew where Olympia Avenue was, you wouldn't have asked me where the school is. So I use off to tell you a major road that the school is near.
Where is your Graphics shop?
It's on Santa Fe Drive.
Hmm, I don't know where that is.
Santa Fe Drive runs along the river.
Directionally, along usually means roughly parallel with. (I could have also said, "The river runs along Santa Fe Drive.")
Now, let's pretend I live where the orange square is, and my friend Monica lives where the blue square is.
Where do you live?
I live on Calais Drive.
Isn't that close to where Monica lives?
Yes, Monica lives just up the road from me.
When giving directions, up and down might be roughly synonymous, and they don't necessarily connote hills. I could have just as easily said down instead of up. In fact, one could even argue that up means "further down the road," and down means "further up the road."
These adjectives are flexible, and can be used in ways other than those I've described here. But I've tried to at least point out some of the subtle differences. I would not say that the school is along Pace Street, but I might say it's down Olympia Avenue.