It's not very helpful to use guitar harmonizations as a way of analyzing tunes that don't come from a tradition of chordal accompaniment. It's clear what the modes used in Hava Nagila are, purely from its melodic structure. I included it as an example in my modes tutorial (in the section on modes not found in Scottish music):

http://www.campin.me.uk/Music/Modes/

That document keeps growing (I've added examples to it in the last week) and this thread has given me some ideas for more stuff to throw in.