I am trying to apply Akaike Information Criterion on a collection of Gaussian mixtures fitted on some data points. My question is, can I use AIC even if the number of components of Gaussian mixtures are different?
Yes. This is exactly the kind of situation AIC is designed for; indeed, if you were comparing models with the same number of parameters, maximizing AIC would be reduced to just comparing likelihoods.
You $can$ use AIC to compare models, and many do. But it's not necessarily the best way to go, and often chooses too many components. See
The general consensus appears to be that BIC tends to preform much better.
What is somewhat surprising to me is that I can't seem to find any papers discussing $why$ AIC does poorly, and the answer seems very obvious: the simple model is on the boundary of the more complicated model. This causes a lot of complications, as is well documented in case of likelihood ratio tests. The parallels between a likelihood ratio tests and preforming AIC on nested models is very obvious. So I'm a little surprised this paper hasn't appeared yet. Maybe I just haven't found it.