In Portugal, ano letivo is the most general expression used. The word letivo originates from lição which is lesson. So, no matter the level of education, it all works with lessons. So that's the general expression.
The other two are therefore more specialised expressions. Ano escolar is used up to and in high school and ano académico is indeed used in all higher education contexts. Education institutions up to high school are mostly simply called as escola (in English, school), so from there the designation ano escolar. Universities and other higher education institutions are also called academia (in english, academy), so it seems to explain ano académico.
Having said this, both on lower or higher education levels ano letivo is always right and can be used.
There is yet another expression which is ano curricular. That refers to following a curriculum which, again, is transversal to all levels of education really. All students follow a curriculum. Nonetheless this expression is used again mostly in higher levels of education because of the less structured character of curricula. What I mean is, university students can opt between different paths in their education, by choosing different subjects in the same area of studies, so they often end up creating their own curriculum. From there ano curricular.
EDIT: The difference between ano curricular and ano letivo is that the first refers only to the study activities (everything one has to do to complete a subject) while the latter includes the first and also refers to all the extra activities (also called extracurricular activities) that happen in that period. Here think, for example, about holidays.
The expressions and their application are correct while the explanation represent my view of things. Should I be wrong, please correct me.