You can also say, " yedi aydan bu yana Türkçe öğreniyorum"
Here are google results:
aydır = 1.460.000 results
aydan bu yana = 768.000 results
aydan beri = 75.000 results
They have the same meaning, but "aydır" is most prefarable one as it is the shortest. "Aydan bu yana" is more used than "aydan beri" (though it is longer) because it is the best choice for official documents, political statements, newspaper articles and so.
As you said, "the most important thing is to be understandable". "yedi aydan beri Türkçe öğreniyorum" makes as at least much sense as the others.
Thanks so much again Scalpel, for your explanations. I was tying to use -den beri that I learnt in a sentence, maybe it would be better to say - Ekimden beri Türkçe öğreniyorum - I´m learning (I´ve been learning) Turkish since October?