Odense has a large selection of attractions and museums with historical themes. The city's history spans more than 1100 years and just about every period is represented at the various museums.
You can learn about the earliest period from around 900 at Møntergården (among other periods) and at Odin's Odense (named for the Norse God Odin/Wotan), and at the latter there are different events and activities all year around in which you can participate.
The Funen Village and the Hans Christian Andersen museums all focus on the 19th century - a century with great development and change, not least social, of which Andersen himself is a good example. His birthhouse, childhood home and the museum are, of course, dedicated to his life and works, but also give a good insight into the general conditons for commoners, just as does The Funen Village for the rural population.
Modern history is richly represented, seen from different angles, at 'Tidens Samling', The Danish Railway Museum, Odense Bunker Museum and The Danish Media Museum.
You can explore the individual museums on this list and decide which you want to visit, if not all!