Most likely older than he appears. In the early scenes showing his family's murder, Slevin (Henry) looks to be approximately ten years old. These scenes took place in 1979, as shown in a caption when Goodkat begins explaining the events to Nick Fisher. Assuming the movie takes place in 2006, when it was released, this would mean that Slevin is approximately 36 or 37; older if he was eleven or twelve when his parents were murdered. Actor
Josh Hartnett, meanwhile, was born in 1978 and would have been 28 when the movie was released.
Goodkat mentions several times that this is 20 years in the making, so one could surmise that Slevin is in his late 20s or 30, at the most. This would make Josh Hartnett's age at the time of release appropriate.