Instead of writing to an SD card, how can I put Volumio onto a USB stick to use with a PC?
Yes, you can do that when the x86 version is ready. A beta will be released together or soon after the PI.
Thanks. Any idea when that is likely to be? What is “PI”?
Current volumio releases are made for ARM devices, see the download page. Future release, Volumio 2 will when it’s ready.
Why not on ARM too?
Of course an SD, eMMC (Odroid), USB Stick or an externel USB hdd will work on an arm device.
The OP was asking for using the stick with a PC.
From that I concluded Volumio on a PC.
Do you mean on USB also on ARM? Why not, but sure not in the short term (as I can’t really see an advantage compared to cheap microSDs…)
Of course Volumio2 will be released for lot of ARM platforms like the earlier one…
USB may have better wear leveling 
I had a third SD card failing in Volumio just yesterday
Volumio2 will be just rock solid in terms of SD Wearing…
But I mean, why not adding that option… What do you use to boot from USB?
I’m still using SD, I have no time to work on it…
As the RPi3 can be booted from an external USB disc (SATA, MMC etc), I’m wondering if Volumio can be burned onto an exxternal disc? That would be great. Ropiee for example can’t boot from anything else than a mSD card.