[Lingo] So happy I cried... writing japanese words

[steven smith <sjs@example.com>]

This started as a question to my japanese instructor.  I asked:
> Is "so happy I cried" something a Japanese would say?  If
> so, how would you say it?
>
> I did a web search and find that 嬉泣 appears often.  I
> can't find a definition for it as a word, but it looks like
> it would mean "happy cry."  If it is a word, how would you
> pronounce it?  うれし・なく?  き・きゅう？

She replied:
> Hi, it is used as a noun...so, "Ureshinaki o
> shimashita." ( I cried because I was so happy,
> so happy that it made my cry)  or "Ureshinaki
> desu"  (I am so happy I can cry.) in response
> to a question like '"are you alright?" by
> people noticing tears in one's eyes.  Usually, the
> context make it obvious.

>From here I started poking around on the web looking at
various ways I could think of to write うれしなき.
Below are number of google hits for each possible way I
could think of to write うれしなき that I can think of:
about 67,200 for 嬉泣
about 13,500 for 嬉し泣き
about 2,640 for "うれしなき"
about 117,000 for "うれし泣き"

My computer interface expands うれしなき to 嬉し泣き when
typing.  In my dictionary I find both 嬉し泣き and うれし泣
き but not 嬉泣.  Also the Japanese online dictionary I use
most (http://www.alc.co.jp/) often doesn't recognize 嬉泣.

I've noticed something like this with other words but this
is the first time I've followed through to see what is going
on.  At this point I'm not sure even what question I'm
asking, but there is something here that doesn't make sense
to me.  Can you guys tell me what's going on here?

Are there really 4 valid ways to write うれしなき with うれ
し泣き being the most popular but 嬉泣 being also very popular.

What does 嬉泣 not showing up in dictionarys say about 嬉泣?

What does 嬉泣 being almost as popular as うれし泣き signify
if anything?

What else is going on here?

Thanks
Steve S.