Hakuouki was released in this order:
Hakuouki Shinsengumi Kitan (or just Hakuouki), Hakuouki Hakketsuroku, Hakuouki Sekkaroku OVA, and Hakuouki Reimeiroku.
Hakuouki Shinsengumi Kitan is the original series. Hakuouki Hakkesturoku is the sequel to the original series. The "episode zero" of Hakuouki Hakkesturoku (Memories in Kyoto) is a recap of the first series. The OVA series was released between the second series and Reimeiroku. Reimeiroku was the third full series released and acts as a prequel to the original series.
To conclude, if you want to watch in chronological order of the show (as opposed to release order), the correct viewing order would be:
- Hakuouki Reimeiroku
- Hakuouki Shinsengumi Kitan
- Hakuouki Sekkaroku OVA
- Hakuouki Hakkesturoku
Edit: First, I actually made a mistake originally. The OVA is actually set in between episodes 8 and 9 of the first season of Hakuōki Shinsengumi Kitan, so chronologically it would really be before Hakkesturoku.
In regards to the movies, their roles are a bit more confusing. According to Wikipedia:
Two new films are scheduled for 2013–2014. Film 1 was released in August 2013 and is released on DVDs February 2014. The film is supposed to be a retelling of both seasons in greater detail and with a slightly different ending.
However, ANN states:
Production on a two-part Hakuōki film project that will open  has been green-lit. The film will tell an all-new story.
Having not seen either of the films, I cannot say for certain where they fall in the timeline.
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