The Thor/Loki/Odin family unit remind me of Elijah/Loki/Mikael. And while I suppose most would jump to compare Klaus to Loki because Loki is adopted and Loki is the "bad" guy I also think that Klaus has parallels to Thor.
Thor is so sure that he deserves to be king and that ends up being his downfall. In anger, Odin casts him out and strips him of his powers, which reminds me of how Esther felt that Klaus was too dangerous and cursed him to block his werewolf side. While both actions were about punishment, Odin only wanted Thor to basically learn his lesson and be worthy of his powers while Esther really didn't want her son to ever regain his.
As for Jane, she changes Thor and it is because of her and her friends that he begins to learn that part of being a "king" is taking responsibility and protecting others, rather than just using your power to trample on others.
Stefan [to Klaus]: Your family wants you dead because they can never be what you are - a king.
I think that this was one of those moments where Klaus felt a real kinship with Stefan and it is one of the things that drives Klaus, the idea that someone would see him that way. In his mind's eye, he always has be prepared for battle.
Here are some Thor quotes jumped out at me at I watched for TVD parallels.
Laufey [to Loki]: Your father is a murderer and a thief! And why have you come here? To make peace? You long for battle. You crave it! You're nothing but a boy trying to prove himself a man.
Thor: I have no plans to die today.
Odin: You are a vain, greedy, cruel boy.
Thor: And you are an old man, and a fool!
Thor [walks up to a pet shop clerk]: I need a horse!
Thor: This mortal form grows weak. I require sustenance!
Jane Foster: Who are you?
Thor: Youa'll know soon enough!
Thor: I will end this.
Odin: I have sacrificed much to achieve peace. So too must a new generation sacrifice to maintain that peace. Responsibility! Duty! Honour! These are not mere virtues to which we must aspire! They are essential to every soldier, to every king! »
Odin: Thor, Odin's Son, through your arrogance and stupidity, you have opened these peaceful realms and innocent lives to the horror and devastation of war...
Here is a quote from Tom Hiddleston about his character, Loki, and it made me think of Klaus as well:
"My job is to find sympathy where society refuses to. People like Loki are often locked up and judged and reviled—and rightfully, kind of, chastised and castigated and lionised. My job is to find the humanity in him. Ultimately, underneath all of Loki’s hatefulness and spite is a lost child. I have to get underneath the skin of that. He's just someone who is so lacking in self-esteem, all he needs is true affection, I guess."
From the cartoon: