My question: The Airport Express has an Ethernet port. Is it possible to access the Airport Express wired to an Ethernet network and use it to listen to streamed audio?
Question two: And still use its wireless functionality to access the Internet?
Yes, you can configure the AirPort Express for a roaming network.
What about the Airport Extreme in this regard?
Yes, you can use an AirPort Extreme in a roaming network configuration; no, you cannot use it for streaming.