Does the letter "X" equals to the sound "Cris"? Why? Like in x-mas or x-tina. No, it doesn't. It's just a convention, a custom, to write 'Christmas' as 'Xmas'. We'd usually read 'Xmas' aloud as 'Christmas'. I've never seen 'Christina' written as 'Xtina'.
X is Chi in Greek, used there as a symbol for Christ. So the Christ in Christmas is sometimes abbreviated as X. X-mas. The holiday itself being a condensation of "Christ's Mass"
You will also see X-ing - meaning crossing. Deer crossing, duck crossing, pedestrian crossing, etc. The place in the road where they are either allowed to cross (in the case of people) or are likely to cross (in the case of animals).
As Vorpar said, X basically is a short of... shorthand for Christ. You'll get a lot of Religious Studies (erm) studiers, writing 'Christians' as 'Xtians', as shorthand.
I think when you see 'Crocodilles x-ing' (for example), it's slightly different, the X representing a literal cross (a non-religious one that is). Possibly the 'crocodille' bit took up too much space on the sign, so they