1. I called Emily, walking along the river.

2. I called Emily while I was walking along the river.

3. I called Emily, and she(=Emily) was walking along the river.

4. I called Emily, and I was walking along the river.
---------------------
Does #1 mean #2, 3, or 4? Which one does #1 usually refer to ?

1 and 2 mean the same thing. They could mean the same as 3 and 4, but those are awkward and wouldn't be used. If you replaced "and" with "when" in 3 and 4, they would work fine.