A coworker of mine the other day invited me to her 21st birthday party and I've been wondering if she ask me go because she likes me. She is cute and I haven't asked her out because if I embarrass myself, I still have to work with her. I also don't know if she invited other coworkers so I'm not sure what to think of this.

If she has invited you to her birthday party then you must go to see how does she behave with you! And it seems that you also kind of like her but afraid to express it. Right? Spend a little time with her and see how does she responses you. That's the only thing you can do to get your answer. Wish you luck ! God bless :)

Why think anything at all about a birthday party invitation, except are you going, and the gift you buy her if you do? How long have you worked together?

I would not think anything of it. She invited you to her party, go or don't go.
How long have you known her?

I have known her for about 8 months. I want to clarify where she stands before I do anything. How can I stumble across this info without being obvious.

Plus the only time I Interact with her this when I'm at work

This isn't a spy interrogation. Interact naturally as a human being and see what happen. If you go to her party, smile, mingle, and have a good time. You know, PARTY! Leave the rest of that stuff alone, and don't force things. If this is too much for you, stay home and wonder and fret. This isn't rocket science so keep it simple.

Or hire a psychic, or mind reader for guidance.

Don't get out much, huh??

It's a party. That Means Other people. Possibly other coworkers. Just go have fun and meet people. If she wanted to get to know you, I would think she would have asked you out.