Barack obama won the presidential election in 2008 and was inaugurated in 2009. inaugurated in 2009, barack obama had won the presidential election in 2008. barack obama, who won the presidential election in 2008 and was inaugurated in 2009. in 2008, barack obama was elected, and he was inaugurated in 2009.

The most correct answer is the first sentence. 

The verb tenses in the second option do not flow. It should instead read: Inaugurated in 2009, Barack Obama won the presidential election in 2008. The third sentence is a fragment, or an incomplete sentence. There should be a comma where the last period is, and then more information (i.e. Barack Obama, who won the presidential election in 2008 and was inaugurated in 2009, served a total of two terms). The last option is not parallel and could be more concise. For example, it could read: In 2008, Barack Obama was elected, and in 2009, he was inaugurated. Or, it could read: Barack Obama was elected in 2008 and inaugurated in 2009.

The answer would be Barack Obama won the presidential election in 2008 and was inaugurated in 2009. This is the best option since it is states an information and it does not need any punctuation marks in order to indicate and emphasize the events.