"I am out of X" or "I have run out of X" is used when you have a limited supply of something which you are steadily using. When you have used it all up and have no more, you "are out of X" or "have run out of X." It carries the idea that you haven't been paying enough attention to the supply and have been taken by surprise. My wife might say to me, "Honey, we're out of bread, could you pick up a loaf of bread on your way home?" Or, "Uh-oh, I we'd better stop at the gas station, we're about to run out of gas." Or "Oh, no, I'm need to get to work and I'm out of clean shirts." In your passage, it is intended humorously. The writer is saying that running out of socks is a "pressing concern." Kurt has these big life issues, but for the moment running out of socks seems more important to him than anything else. Perhaps he doesn't want to think about the big issues and allows himself to be distracted by a small issue.

It also makes him sound like a snob. Hahaha

It is tongue in cheek. It means he had no other pressing conerns. : )

By the way, you say you are out of socks when you have no socks left to wear. Maybe they have holes in them. Maybe you lost them. Maybe they aren't clean and need to be washed.

They are making a joke. They are saying that he didn't have any socks to wear cos they were all torn and that his issues with his socks was more important to him than all the attention and fame that he was receiving. Hehehe So funny actually.