For information on the Irish try here:

http://www.faqs.org/faqs/cultures/irish-faq/part03/

Nollaig is the word for both Christmas and the month December, and sona/shona is the word for happy, as Gaeilge.

The first is pronounced (roughly approximating here) "no lug" and the latter "h-yun-a" with "yun" rhyming with English "run" but you barely pronounce the "y". I'm sure a native speaker could describe the pronunciation better than I.

"Nollaig Shona" is the generic greeting, such as you would find on a Christmas card. If you are addressing people...it gets a bit more complicated, depending upon how many people you are addressing, how you want to address them (ie formally or informally, etc.)

Considering your limited command of the language, I'd definitely stick with the generic form. It's just easier for everyone that way.