Any longer and any more (or anymore) are synonyms.
When we use any longer or any more, we need to use don’t/doesn’t because the adverbs express a negative relationship with time. It is also important that we put them at the end of the sentence.
However, when we use no longer, it comes between the subject and the verb. Unlike any longer and any more, it is used in positive sentences because it makes the sentence negative.
I don’t drink coffee any longer.
I don’t drink coffee anymore.
I no longer drink coffee.