I have a section for "refereed publications" and one for "other publications". Where should I put publications that are presently in submission? Is it OK to put them in "refereed publications"?
If you submit them to a journal that will referee them then put them in the refereed publications and mark them "submitted - under consideration" or similar. Just make it clear.
And update the CV as needed if you get accepted or rejected.
An alternative, if permitted, is a third section for submitted work under consideration or even work in progress with submitted works tagged as submitted. My preference (for myself) would be "Work in Progress". Sending that signal can help you.