virtualbox.org

I have a MacBook with not very much hard drive space. I would like to install my Linux guest OS on a 16 GB USB stick - the whole thing on the USB stick so that it boots from there, not just the storage. The VirtualBox installation itself could be on the Mac - just the virtual machine on the USB. So far I haven't found an option that allows me to install it there or move it there after installing to my Mac hard drive. Would appreciate any help - I am new to VirtualBox but I use Parallels on my main desktop.

Have a read of this earlier thread. The linked thread discusses a different host, and SSD rather than USB, but those things don't matter.

It will work, but assuming it isn't USB3 then you can expect performance to be poor. At least you won't have the Windows host problem of changing drive letters.