You must be desperate when solving "out-of-space" problems by deleting files from the disk ... I can understand children who want to install another game, but don't have enough space so they decide to DELETE directories they think they are irrelevant. If anything goes wrong, well, never mind ... FORMAT c:\ will do the job, and everything will be working even faster.
But in the era of unexpensive hard disks and keeping in mind that you are not dealing with computer games but a database, why don't you buy another (large capacity) disk? How long will this "delete" operation last? What will you delete next month?
"Stage" directory ... if I'm not wrong, it can be found in the Oracle installation set; it contains, among other things, the "product.jar" file which is used by the Universal Installer. When the product is installed, there's no need to keep the WHOLE Oracle installation directory on the disk (not only the "stage"). Therefore, if we are talking about the same "stage" directory, it might be harmless if you delete it.
Don't do that until you hear at least another opinion, as I'm not a DBA. I guess they will know better and tell you for sure what to do.
My final answer would therefore be: buy another disk.