I think the best option for you is, "Over the period of 2000 to 2010" Also, "over the period" and "during the period" are almost the same, and the difference between them is very subtle, and I'm not sure which one is better to use without knowing the rest of the sentence. Also, while there's nothing wrong with "over the period" or "during the period," we normally won't say that. We might say it if we're trying to reach a word count on an essay, so it makes sense to say it for the IELTS, but in conversation, we would just say, "From 2000 to 2010." It's also perfectly acceptable to say this in an essay. I hope this helped. :)

over the period from 2000 to 2010

Of course I don't know what your context is, but you could ask yourself if you need the word "period" at all. It should be used to connote a length of time in which some extended event, or series of events, or something on a cycle happens, and arbitrary date ranges would of themselves wouldn't constitute that. In which case, I'd simply say "from 2000 to 2010" or its more succinct version "2000-2010". But let's suppose you do want the word. You don't need "of" following it; that would be used to say something like a "period of years". Just put the date range in appositively as in your second or third example. As far as "over" or "during" goes, I would use the former to describe something that related to the period in aggregate, or compared the end to the beginning -- e.g. "world population increased by XXX% over the period" -- and the latter to talk about something that happened at the same time but not necessarily coterminously -- e.g. "the company went from start-up to IPO during this period". "In" is also a likely choice: e.g. "15 companies were founded in this period".