The AICc values make sense in relative terms (not in absolute terms). I would say the same for the deviance. The difference in AICc between two models says how much relative support has one model with respect to the other. The difference in deviance between two models says how much deviance is explained by one model with respect to the other (in case the two models differ in just one "covariate", it is how much deviance that covariate explains). If the number of parameters is too high or not depends on the degrees of freedom you have (i.e. it has to do with the sample size).
A first starting point to understand if your model is overfitted is checking the standard error of your parameters' estimates. How large are the 95% CI of those 18 estimated parameters? Another relevant issue is the extrinsic non-identifiability of your model that is the parameters that the model cannot estimate due to "problems" with the data (relative to the model you have set up). Regarding the latter, you may want to have a look at 4-71 (Addendum – counting parameters) in the Program MARK – "A Gentle Introduction". You may want to have a look at a recent post on parameters identifiability
here.