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It seems very socially awkward to open people you've been introduced to.
...why is that? They were introduced to you so you can get to know them. If you were back at the graduation party, a simple opener could have been:
"...so how did you meet
(insert name)? Oh really? I remember when I first met him/her. We were on the playground at school in 3rd grade and..."
As far other house parties go, just throw yourself out there. Walk up to a girl and just talk. "Hey, how's it going? I'm
(insert your name)". It's nothing elaborate, but do you know why they will converse with you? People go to parties to SOCIALIZE and MEET PEOPLE. That's how it is especially in college.