Hey Chris,
:bravo: for showing some interest in one of the local Formosan languages. I studied Linguistics as an undergrad, now I am doing a Master’s at NTU in Computer Science, but language has always been my passion. I’ll share some of my knowledge and experience studying Atayal. First of all, I am not sure why it is written as Atayal, because all of the Tayal that I know pronounce it as Tayal, so if someone knows why, please share! 
Also, the “l” at the end of a word is pronounced as “n”, and “t” sounds like a “d” in English so you get “dai-yan”, which means people, like many other languages, the name of the language the given by the natives is often “people” or “the language of the people”.
In terms of resources, this is a common problem in any language that has not been well studied, is dying, unpopular, etc. Studying a language without many written resources can be a true challenge. Most of the resources are either quite simplistic or linguistic. This essentially leaves you with two choices: you can learn linguistics to take advantage of the resources that are available (and there are a number of good linguistic resources for Tayal in English and Chinese), or try to learn it solely by conversation with Tayal, which is not an easy task because many speakers nowadays are only partially fluent, unless they are 60 years or older, and will probably not be able to tell you anything about the grammar. You might check out one of the Tayal churches in Ulay, some of them may do service in Tayal, and I believe there are bibles written in Tayal, but I have not been fortunate enough to get my hands on one.
I actually have a Tayal dictionary “Atayal English Dictionary” by Soren Egerod. I think it was written in the sixties. Anyway, I think it’s extremely hard to get, I found it used on Amazon.com and it was the only copy available, cost me about $75 US, so I am considering scanning it all into pdf since it is essentially unavailable. Just to make things more exciting they are two main dialects of Tayal (differ slightly in grammar and pronunciation), and many local variations in vocabulary. There are quite a few Japanese words that made their way into Tayal (much like Taiwanese). My girlfriend is Tayal and she is also what I can consider partially fluent, she can understand most of everything people say, but in terms of speech she usually just peppers her Chinese with simple nouns, verbs, or simple sentences. Anyway, here are a few words for you:
( denotes stress) Jilala (jee-la-la) - Let’s go
Avila (a-vee-la) - Let's go to sleep Agai! (a-gai) [it’s a fricative g, so a bit softer] - Ouch! (this word you will hear a lot if you hang out with Tayal)
Nanu (na-nu) or (na-nu) [I have heard both accents] - What?
Mami (ma-mee) - Rice Mit (meet) - sheep Hogin (hoe-geen) [g is fricative, otherwise it means “dead”] - dog
Mugan (moo-gan) - Taiwanese person Thiluw (tey-loo) - Mainland Chinese
Talax Tunux (da-lah du-nuh) [the x sound is fricative like ch in Bach] - foreigner (literally red head)
If you learn anymore, please share!
