Ayla 1

Ayla is also a Turkish name. It means "halo" in Turkish.

The Hebrew word for oak is Alon, which is a seperate boy name. In Hebrew, the name Ayla does not exist as far as I know, especially not as a feminine form of Alon. The Hebrew spelling you've got there is Ela, which means, as clevelandkentevans said, terebinth. And it isn't pronounced Ayla, but eh-LAH. So you should remove this, I think. [noted -ed]

In Latin, 'ala' means 'wing'.

Basically this name means "strength" or "strong authority". A possible root (in Latin letters, "AYL") means something along the lines of "strong" - related to "oak tree", "pillar", "stag deer" and "chief" - but moreso to "ox". Another root ("AYLH") means "strong one", related to a hind or deer. Also, there are six words in Hebrew that mean "oak". One of them is "Elah", which has been translated as both "oak" and "terebinth". These translations are difficult, mostly because words with ancient roots may change slightly over time in meaning or pronunciation, such as Greek has.

According to the following website about plants in Israel, Elah is the word for terebinth and Alon is the word for oak tree, which first in with Smadar Shir Sidi's _The Complete Book of Hebrew Baby Names_. So I really question whether or not Ayla can mean "oak tree" in Hebrew.
http://www.n-k.org.il/pub/publications3.html