I have to admit, I am not a very good PUA. Right now I am living in a horse ranch with a 1-hour drive to the city so pickup has been put somewhat on hold. Plus, such long time away from the city really brings back approach anxiety. How would you go about it if you visited the city every 10 days or so? Plus, where I am in Bogota, Colombia, people tend to have a rock-solid ice barrier and are rathe cliquish.

Back in college, which I will return to after this GAP year there is a party every Tursday night, but it is a small Art College. One of my friend( who is a natural) says that it is really tough to hook up in the parties.

Since the school is small, second encounters are kind of awkward. I just maintain myself give a smile and a wink. Usually I went and chatted up a cute girl during lunch and have a mini-date. But they always went away.

For someone who never had any success before, I was able to get a few numbers and a few smiles and even got laid, but was still chasing girls.

One especially embarrassing experience was this girl who I came across a few times, and chatted her up at a party while she was in a group. I was joking around and even negging her a bit, but she looked at her friends as if she was saying"what is up with this creep?"

How would you guys handle these situations?

I'd make it worth my fucking while and get in as many approaches as I could.
The key word here is they tend to. Not everyone is like that, so find the ones who aren't. All this means is you have to approach more - that's it. Remember, if they're cold towards you then they're not worth the effort. Just move onto the next one and thank your lucky stars you didn't have to put up with them any longer than you had to. This isn't a family dinner and you're obligated to put up with their shit. If they're not nice, fuck 'em. Move along.
So don't focus on hooking up and just have fun at the party. Let the chips fall where they may.
They're awkward cos you make them that way. After you've kissed or slept with a girl and you see her again just be friendly and make small talk, and talk about doing something again if you want. That's not awkward, it's normal.
First of all, don't chase girls. Guys who chase girls do so because they have a lack of other options (major turn-off... no girl wants a guy no other girl wants) or because they value that particular girls time and attention more than they should (raises questions in her mind as to why).
As for that experience, either it was all in your mind or she was just a bitch and needed called out on it. "Why do you keep looking at them like that?" - let her answer, and if she is bitchy then just smile and say "oh, you're one of those girls... haha, fuck that." and walk away.