Generally, British English often keeps words separate in a compound noun such as this, while American English is more likely to run them together eg back seat, apple sauce (GB) backseat, applesauce (US). As for the stomach ache example, I'll admit that GB Eng is a little inconsistent here. After all, we often run toothache, backache and heartache together, so why not stomachache? I would guess it's because it looks so strange. The 'achache' at the end makes you think of a jolly Latin American dance or something - which sounds far more fun than a stomach ache anyway! And yes, I'd agree with Stephanie that we wouldn't hyphenate the two words.

There are two accepted spellings of this word, the first two of your examples. I have never seen it as a hyphenated word, so that last one is unusual to me. There are many reasons for the accepted alternate spellings of words in English, including the different origins of words, sometimes British or American. This one may be due to the fact that the two words are often used together so they come to be spelled as one word, perhaps.

I would only use the first one - two separate words. The other two don't look right to me.