My greatest strength in terms of relationships is power, in the sense of purposed interaction such as teaching, giving a presentation, DMing a game, leading a team, etc. So I usually socialize by playing games or doing some sort of project with others. It helps that I am very good at explaining games.
My big weakness is around a lot of people I don't already know and without a specific purpose, such as parties. I vastly prefer giving a business presentation or having a meeting to a general party.