Dear V.,
I know it sounds trite, but try sitting her down and telling her 'what's what'.
Being a former 'wee hours' person myself, her being tired does not help the process - so catching her as soon as she's up for the day is best - she is more likely to be alert (grumpy possibly, but alert).
I am suggesting that you bring a pad of paper - either doodle to keep your cool, because chances are you'll lose it if she doesn't respond favorably - or write out your terms and/or conditions for her getting a job and moving out. Having decided these things ahead of time will help your case immensely - she will understand you've thought this out and are at the very least serious.
Being upbeat about helping her figure out her finances (she being a student has only done it on the short term, I'm betting :) , what will get her through the next week to month), where she can look for an apartment, what she might like for a job, will only help YOUR cause to help HER get on the track you're looking for.
Avoid 'bank of Mom', mention of her place in yours, particulars of how to make everything work, in short, only discuss what is going to happen, and a time-frame. Only after you have finished this discussion and **she has made a decision do you offer any suggestions for anything else.
I'm sure she is due to graduate soon, and while you are softening up her introduction to the real world, you are in fact going to aid her in as simple a manner possible rather than insist she simply get out. I understand you don't want to alienate her. Concentrate on your goal rather than being friends - the friends part will come.
My Mom went to work every day, came home to see me in a state she didn't like, talked to my Dad, and Dad set it out for me, find a job. He didn't have to threaten me with kicking me out. He simply said I had to pay my way if I were to live with them. He gave me a flat rate, board (which were VERY low, but to someone without a job, impossible) (not room, which he would have had to pay taxes on :). There was no arguing with him, either. I tried saying that I didn't eat much, and that there was this and that, and he simply stuck to his flat rate. (He didn't even have to mention taking it or leaving it. I think that would have set me off if he had, actually, now that I think about it).
You might also open her eyes as to the reality of those college loans. They come due - and the government is tightening up on those who think they might just default, get a bad credit score for 7 years, and start new. They come due - and things change when you miss a payment. If you need to, take her to the bank, and have the bank show her what she will need to do to pay off these loans. It is quite daunting at first!
Good luck! And remember: She's an adult already.
M.