It's a word put together from Chillin' and Relaxing. It actually means the same. If somebody should cool down you could say he or she has to relax or has to chill out. If you decide not to choose between these to, or you haven't made a decision while you already have to say the word, you say 'Chillax'.
It could also mean having a good time with your friends.
Chillagy refers to " Trilogy" which is a set of three works of art that are connected, In this case you chill for 3 days straight. There are no breaks and you must remain with atleast 2 other people.