Ok, so I was looking at that second Oriole, and thinking that it didn't match up with the pictures of the female orioles in the bird books. I determined that I had a young male oriole - a different bird than I had seen previously.
This afternoon I saw a female oriole for sure. She looked like the ones in the books - no hood on her head like the males do. The young male was in the tree at the same time. His belly isn't as orange as the first male oriole, and his head and wings aren't as black. So, in just a weeks time I've seen three different orioles. This is very exciting!