But since her entry was verified by a Immigration authority ie port of entry, and she has a D/S(duration of stay, valid till her stay) on her  I-94 she can adjust her status through marriage (only marriage, that's the only way ) with a US citizen as immediate relative. But if you marry her right now (I am not saying not to ) she has to live in the shadows, and wait until you get your citizenship.  

Any other applications you submit on her behalf to the immigration would make her deportable, and she would be served a 60 days notice to leave the country and if she don't she would be committing a crime (immigration violation is not  a crime, but only a civil violation but when the USCIS serves you a notice; it would be a federal crime).

She can't file for asylum because she has exceeded the 1 year time limit, but she can apply for withholding of deportation based on convention of torture which she would be granted. But the problem with withholding of deportation is, you will be given a SS number, EAD (which has to be renewed every year) and you can't travel outside USA. If you do, that would serve as a voluntary departure (because she is  out of status you are deportable).  Also if you are granted withholding of deportation, you will never be able to adjust your status (as per the current law).

So if you love this girl and you wanna marry her, then you can go ahead and do that in your county court, but she has to lay low and wait until you get your citizenship.

If this your true love let these things not bother you ....Good luck