Cowell, Mark W. A Reference Grammar of Syrian Arabic. University of Michigan Press, 1964. GoogleBooks
Ryding, Karin. A Reference Grammar of Modern Standard Arabic. Cambridge University Press, 2005. GoogleBooks
Stowasser, Karl, editor. A Dictionary of Syrian Arabic (Dialect of Damascus) English-Arabic. Georgetown University Press, 1964. GoogleBooks
These three books are the best investments you can make, I think. The first two are so comprehensive (yet also down to earth) that they literally contain the answers to 99% of my questions. If you are trying to sound less like a news anchor and more like a normal person, the dictionary is highly recommended even though it’s a bit old. Unlike a formal dictionary, most words you randomly flip to will be really practical.
Foreign Service Institute course
Text and audio; one of the best resources for improving your pronunciation. Hearing an American and a Syrian take turns just pronouncing /t/ and /d/ definitely helped me.
On the continuum between fus7a and amiyya, this blog is willing to look at the most informal sources possible like memes and morbid/dirty jokes – which they then analyze in a very meticulous and effective way!
Defense Language Institute: Phone conversations in Levantine Arabic
Hear native speakers conversing as normal people. Someday, perhaps we will sound like normal people.
Reverso Context: I use this site every day.
Brustad, Kristen. The Syntax of Spoken Arabic: A Comparative Study of Moroccan, Egyptian, Syrian, and Kuwaiti Dialects. Georgetown University Press, 2000. GoogleBooks
An interesting but rather complicated book. I have found it to be a bit overkill since I’m learning one dialect, not four!
Huxley, Henry Minor. Syrian Songs, Proverbs, and Stories: Collected, Translated, and Annotated. Journal of the American Oriental Society, 1902. Archive.org