I don't often read

[Rachel Adams]

Does each sentence convey a different meaning?

1. "I don't often read short stories."
2. "I don't read short stories often."
3. "Often I don't read short stories."
4. "I often don't read short stories."

 

[Yankee]

I would expect to hear/read 1. or 2. (in that order). Seldom/never for 3. Seldom for 4.

 

[emsr2d2]

If you were to use #3, you'd need a comma after "Often".