Can a Demon get into the sickened condition, e.g. by the sickening offensive investigator talent?
A creature is not immune to a condition unless an effect makes the creature immune to the condition or the condition says that such a creature is immune to the condition. This includes the condition sickened. The general descriptions of the condition sickened and of both outsiders and demons grants demons no general immunity to the condition sickened. Specific demons may exceptions. (I mean, really, there are a lot of different kinds of demons!)
This means that, for example, the investigator talent sickening offensive, an extraordinary ability, can give the typical demon the condition sickened.
Note: While it may seem odd, a condition is often not literally representative of its name. For example, an investigator that uses her sickening offensive talent to cause a demon to gain the condition sickened is probably not giving the demon a brief, nasty cold but, instead, striking the demon in a region that's so important to the demon (use your imagination… or, y'know, don't) that the demon suffers in the same way it would were it actually ill.