How are the different types of songs played. Where are the accents? are there special rythms? 
Hi thereāI am just a beginner on the whistle but I think that what you are calling a āsongā, which is a tune sung with words, might be what would usually be called a ātuneā, which is a melody played on an instrument. There are tunes written for dancing to (dance tunes) and there are tunes written for singing to (airs).
At this website you can hear examples of some of the more common types of tunes:
http://www.whistletutor.com/beginner.htm#1
The first website has a more in depth discussion of different types of tunes. I donāt know how authoritative it is, but it would be a start:
http://www.irishtune.info/rhythm/
Obviously, it would be best to hear the tunes described. He gives many recordings for each type of tune, you might be able to find clips or midis (not a good substitute, butā¦), or sheet music for some of the tunes.
This website lists some good books to read. I actually have two of them on order myself:
http://www.itma.ie/home/leaf4a.htm
Once you know the basic idea of what a type of tune is, then you need to listen to them and soon you will be able to identify what you are hearingāwhether it is a jig, a reel, etc. It is a little hard sometimes because they play so fast, but that is why listening is important. You start to recognize the patterns, but it takes practice when a person hasnāt done it before just like anything. You are on the right track to ask these questions.