A couple of things come to my mind, in addition to a lot of what has already been suggested. In case it affects your perception of what I have to say, I’m a 28 y.o. married, slightly overweight woman with crappy social skills.
I think your friend is a What Not to Wear candidate, and perhaps a How to Drink In Social Settings candidate (if that show were to exist!)
You mention that she wears khakis and button shirts, and never wears revealing clothing, and I really think this would affect how people who haven’t yet met/spoken to her might react.
To me, khakis and button shirts are office wear, though particularly stuffy and conservative office wear (I realise that KC is probably more conservative overall than Montreal, so it might not seem so extreme there!), and if someone in a social setting (bar or even school) dressed like that all the time I would think that they didn’t really know how to dress appropriately for the event, and they never thought much about how clothing can make them more attractive.
When you say that she never wears anything revealing, what extent does that go to? To her, is it “revealing” to show too much arm? shoulder? a bit of chest, like a v-neck shirt? cleavage? legs/knees? clothes that flatter her form/curves? If her clothes are loose and boxy (I’m imagining also not very colourful shirts), that could be a major turn off for people, and they might not even be able to point to that and say “it’s her clothes”. What’s wrong with wearing a pair of jeans and a t-shirt once in a while? Or a sun dress, or slacks and a flattering blouse?
It sounds like she’s (possibly) just not doing anything to make herself look good, and then stands around wondering why people don’t look at her. It also sounds like her standards are high, so when she’s at a party/bar watching people, she might have a judgmental look on her face as she evaluates the suitability of their clothes, tattoos and teeth. So here’s this awkwardly dressed person making superficial determinations of others - that really doesn’t come across well!
About the alcohol; she sounds really juvenile about that. Did she just recently start drinking, and is still in the “look at me, I’m cool, I’m drinking alcohol!” phase of learning to handle her liquor, because that’s what it sounds like. I’m going to guess that when she drinks, she likes to get hammered. Asking why others aren’t drinking, teasing strangers for drinking water; these are things new drinkers and drunks tend to do. It is incredibly Not Cool and I can’t blame anyone for wanting to get away from that. People can see that she has a drink in her hand, she doesn’t need to ever be talking about it. Drinking only things like Mike’s Hard Lemonade is a little weird too, but I’m a beer and wine drinker and I enjoy a good martini once in a while. Alcohol doesn’t make a party; the people do, and she needs to understand that.
And learn to flirt. And smile more - smiling at people is generally a good way to get them to at least smile back (I know you’ve said nothing about her smiling or not, but it’s a fact anyways).