This situation may sound innocuous to some, but I understand how a situation like this can escalate into something seriously ugly. Have any of you ever watched Fatal Attraction? Men, if you haven't, then you should. Ladies, watch it because it's a good movie and Glenn Close is the perfect example of “what not to be when you grow up”. No one should have to worry about boiling bunnies while they are at work!
So here is my .02 worth…
The correct way to address this situation:
1. Document, document, document…. Print out all of the IM's, especially those where she discusses going out together after hours. This phase is called “stacking ammo”. And you need to make sure yours is stacked correctly or it will all blow up in your face.
2. Wait until she is seated in a meeting room before you even walk in. Make an excuse to visit the men's room or make a phone call, whatever you have to do, just make sure you do not sit next to her. If you have no choice, then at the first opportunity, give up your seat to someone else. (Watch the piano recital scene in You've Got Mail to see how Tom Hanks handles the situation.) Avoid physical contact at all costs.
3. Once you have sufficient, written, evidence, tell her that you appreciate all of the attention she has been paying you and that it has been really good for your ego, but you are not interested in anything other than a professional relationship. Make sure you have an exit strategy just in case she loses her sh*t and nuts up on you. You shouldn't have to worry about flying office furniture and paperweights, but unfortunately, you do in this case.
4. If her response is anything but professional and appropriate, then take your documentation to HR or your supervisor. If at all possible make sure the person you present your case to is a woman. Another woman is probably going to be tougher on her than a man, or at least I would be. Once you have the documentation and you provide them with a COPY, they will take you seriously, regardless of gender, simply because they don't want a lawsuit.
The Stupid way to address this situation:
1. Scratch your crotch in front of her and quietly tell her that some girl you went out with the previous night, must have given you a bad case of something that Ivory soap won't wash off. Childish but effective.
While I think some of the responses to this situation have been funny, I'm sure they are not humerous at all to the OP. I will concede that there is still a lot of gender bias in this area, however, I don't believe for one minute that a woman, who has legitimately filed a claim for sexual harrassment in the workplace, would be compensated more than a man if the roles were reversed.
Good Luck to the OP!