Why do people sometimes substitute x for letters in a word?
In those three examples, there are three different, albeit related, reasons:
Xing = Crossing. The "X" replaces "Cross" because an X is a cross.
Xmas = Christmas. The "X" replaces "Christ" because the cross is a symbol of Jesus and because X (really Chi) is an initial for "Christ" in Greek (Χριστός).
Xfr = Transfer. The "X" replaces the prefix "trans-" as it implies a crossing of something.
They are all abbreviations. I would be surprised if the origin of "Xing" wasn't in street signs, where "crossing" would be a long word to print to be able to read at a distance. I've more often seen "Xfr" as "Xfer"; it is used in electronic communications as jargon. I don't know the origin of "Xmas", but some people would have you believe that it's an effort to remove Christ from the holiday. I would guess it is just another general abbreviation.
Xmas is a specific case of using X to denote Christ, a practice that goes back many centuries. One can look up further details, but essentially it's an initial. Imagine if you were documenting the daily activities of the President of the United States, lots and lots of things Barack Obama said and did. Especially if you were writing it out with a quill pen, you might quickly start abbreviating using B to mean Barack Obama. "Secret service guarding B cautioned. .."