Amazon Echo and Google Home are Bluetooth-enabled speakers and voice-command devices. You may be able to stream audiobooks from the OverDrive app to an Amazon Echo or Google Home like you would with any other Bluetooth speaker. However, OverDrive does not officially support streaming audiobooks from the OverDrive app to these devices at this time.
For help using Bluetooth with your Amazon Echo, check out Amazon's help article about pairing your mobile device with Echo.
For help using Bluetooth with your Google Home, check out steps 1 and 2 in Google's help article about playing music on Google Home.