The Edison doesn't have an audio output that provides the signal for a speaker. However, it has an I2S interface that you could use for audio applications, but you would have to add more hardware than just the speaker. If you are interested in the I2S interface, I recommend you to check the following document: Audio Setup Guide for Boards and Kits
The following thread and links might be of your interest as well:
- Intel Edison - I2S Audio Setup
- Intel Edison - Simple I2S Audio Setup - Malinov Family Web Presence
- Audio Block for Intel Edison - Malinov Family Web Presence
The other ways to play sound would be the ones that you already mentioned: Bluetooth or USB.