Which one is grammatically correct?
I worked at X company ...
- from Aug 2005 to Sep 2007.
- from A up to B.
- from A until B.
- from A till B.
- between A and B.
All are grammatical. If you’re looking for advice on which to use, the first is the simplest and likely to be suitable in most contexts (although I prefer to write the names of months in full in formal writing).
You should say Aug 2005 through Sep 2007:
through 4. —used as a function word to indicate a period of time: as a : during the entire period of [all through her life] b : from the beginning to the end of [the tower stood through the earthquake] c : to and including [Monday through Friday][ [MW]]1
Edit: According to this reference, Aug 2005 through to Sep 2007 is "sometimes used" in British English.
From Aug 2005 to Sep 2007 is grammatically correct. I have used it quite a lot when I am writing my CV and I haven't got any problems with that.
Edit: By all means I have to make myself more clear. Imagine a timeline and A and B are just points there. When you are saying I was working for company X from A to B these are start and end points of a segment of the timeline. Until, till and between are used when we are talking about activities so referring again to the timeline we are just comparing segments or periods of time. The suggestion below for through indicates period of time too. They worked through the night. --> The period is the night, but this is a period with a name. We have substitute the time from dusk to dawn with the word night.
Since these are most commonly used in CVs , you can use "From A to B" in most of the cases , or You can also use "From A till Date" when you are still serving in the same company when you wrote the CV or you are referring to your present company. But i don't think the last one where you use Between would seem so right.