May "offsets" be used in mixed-effects poisson regression? Mixed-effects poisson regression studies counts for example of the incidence of a disease given the individual's random-intercept/slope. Mixed-effects regression studies individuals rather than populations. If I used an offset term in mixed-effects regression, let's say to study the incidence of disease per 1000 people via specifying an offset, and used a mixed-effects poisson regression, am I doing something contradictory, and should have run a gee instead? 
Therefore, may "offsets" only be used in glms and gees?
 A: It's easier if you think of a statistical model as having a left hand side and a right hand side.
The left hand side is concerned with what is being modelled. 
The right hand side is concerned with how the modelling is done and what it means. 
In all three types of models you mentioned - poisson regression, poisson GEE and poisson mixed effects - what is being modelled on the left hand side is a count variable (e.g., incidence of disease). 
If this count variable is assessed over a certain span of time (or space) then the time (or space) can be logged and included as an offset on the right hand side of each type of model. This way, the model will be concerned with estimation of the expected incidence of disease per unit of time (or space). The idea of the offset variable is to make the expected counts comparable by relating them to the same unit of time (or space).
Poisson GEE models and Poisson mixed effects models differ in terms of the interpretation of the effects of predictor variables included in the right hand side of the model. Poisson GEE models produce population-level effects, whereas Poisson mixed effects models produce subject-level effects.
