I wasn't using ASIO drivers; my Driver Mode was set to WASAPI Shared, but I could only select one USB input device at a time.
When I set the Driver Mode to MME (32-bit) everything was automatically un-greyed and checked, and I was able to record and monitor all of my inputs simultaneously.
The other modes either had greyed-out devices, incorrect or unlisted devices, or did not record some inputs correctly (i.e. the audio was severely distorted.)