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we are in the same situation

I suggest that you join some sport club or association. You will soon get linked with many.
Go around university area where it's quite alive and dynamic, enter in a bar in the evening and I am sure you won't get alone long time as the Korean like to drink and are open to talk easily when they are in a group and they see a foreigner alone next to them. Maybe the next next week-end you will be sitting for them at the table for dinner or go to the mountain......

I lived in Mississppi and I also had situation like you guys.

I didn't had any friends. and..I hate parties. It is so uncomfortable when I talk with strangers.. etc..

Don't try too hard to make friends. I mean it's really hard to make friends...unless they have something in common with you. I got really closed to my friend who is american because she loved Korean food. I made her some Korean dishes and we kinda talked and became really good friend. I still talk to her . Try to find someone else that connects with you. There's always gotta be someone who has same taste in something!
Good luck!

What about links to sports clubs, classes, etc? Anyone got any information on specific stuff going on to get out of the house?

I made lots of friends through my soccer team here. Sparta Busan, if anyone likes to play soccer you are welcome to join us