I really want to come up with an intelligent answer for this but the only think that pops into my head is the Universal Translators from Star Trek. Despite the fact that they are the comm badges worn on the chest everything everyone says is translated and understood perfectly!
Yeah, but that still doesn't explain how the aliens in the original series all spoke English. Even Spock says a few did! Though they did address that in Deep Space Nine once or twice. And Klingon still comes out sometimes as Klingon, even though the most famous word (which I can't remember how to spell) translated to "Sucess!"
Ok, back on topic.
Interestingly enough, originally the Andalites were suppose to have a sort-of mind-reading ability, too. Like if someone thought "loud" enough, an Andalite, or even someone in morph, could pick it up. The ability to send pictures associated with words may have stemmed from that idea.
However, that random fact still doesn't explain how Ax learned English. Though these theories are pretty good. I have one, however.
I think that all universal translators are connected. So, if one translator knows a language, so do all of them within a few minutes to a few weeks, depending on the travel time for the signals. Then, whenever the person is in morph, the translator takes the thoughts and translates them from the brain to the mouth. So, while the speaker may be thinking in Andalite, he or she will automatically have it translated to whatever the native tounge is.
As for reading...maybe he watched his TV with subtitiles?
Though he understands an Almanic in book 8, he has some trouble with reading the English in book 9. So, obviously his reading ability when it comes to English is not perfect.