Thor does sometimes use older pronouns like "thee," but most writers over the years have gone without them. Stan Lee created Thor using regular pronouns and, in fact, speaking pretty much like a regular, modern-day person. The Don Blake persona still had a lot of influence on Thor's mind in the early days, though, so that may be the reason for his eventual change in speech style.
But he's back to normal pronouns now under JMS, which I'm glad for. Frankly, most writers don't know how to write "ye olde-speak" any better than Knaves, and some write it considerably worse. It's so easy to parody because so many writers have f***ed it up over the years and made Thor come off sounding like a goofy Renaissance Fair actor.