My guess:

Will women receive more power in society because they are more sought after?

No, they'll receive even less power, because they become scarce goods and thus commodities and thus less empowered as people. The ability of a guy to get his pick of the women or maintain multiple women at the expense of other guys will become a status symbol, and nowhere in that picture does one see respect or empowerment for the women.

Will societies 'losers' unable to find wives become resentful and prone to violence or substance abuse?

Yep, as has always been the case.

Will new types of un-orthodox relationships become more common?

Depends what you mean by unorthodox.

Will marriage/divorce rates increase/decrease?

See point 1. I'd wager divorce rates will decrease, though marriage rates will increase (women should have no problem finding men).

Will men leave for other nearby countries for a better chance at finding a spouse?

Almost certainly, especially if the alternative is staying in a lonely environmental shithole.

I think you are missing a very fine point. The wealth gap in China is the only factor that comes into play. Men who cannot find a wife will almost always be in the working class. The middle and upper classes will be fine. Since China treats their working class so poorly, there will likely be no effect on their society socially.

One of China's biggest fears as a nation is the unrest among the working class. They are the backbone of China's manufacturing economy. This is the only thing I would worry about.

Women will not have better or worse rights.

Marriage rates might follow the path of South Korea or Japan and fall precipitously anyway. Mostly because women earning major money don't seem to have the urge to rush into deeply patriarchal relationships.

That and it would seem that age discrepancy would increase between hetero pairs. I.e. mortgage their 'future' partner availability.

It's pretty unprecedented (as far as I know).

I'm assuming they can just live normal lives? We have millions of males/females who choose to be single, so I don't see the entirety of this group being upset.

There is a difference between dating single and non-dating single.

It's been pretty normal in European history for a fifth to a third of women to go unmarried. They didn't date; dating is a modern invention.

Having a lot of single people is not some historically novel development that obviously implies upheaval.

Exactly. If anything I think that there's a certain level of habitat healthiness that is taken on a subconscious level. People regulate their own numbers one way or another at some point (hopefully).

Maybe when/if Japan is half of it's current population (http://japandailypress.com/people-prediction-tokyo-populatio...) [Tokyo's in 2100], then we'll see that number start to grow again.

For cultural reasons, this is a recurring pattern in Chinese society. IIR my Chinese history lessons, it was usually followed by costly border wars and massive building campaigns to thin out the herd and quell domestic unrest caused by too many men milling about with nothing to do and nobody to do it with.

There is a simple solution: polygamy

i think you mean polyandry. polygamy would make the problem worse.

most likely, the men will leave in search of a better life. or stay at home and cause trouble. or the government can organize them in some fashion - military would be an obvious one.

Polygamy means marriages with more than two people. Polygyny means multiple wives, polyandry means multiple husbands.