If I am reading your post correct, your /oracle directory needs additional space. Assuming that your vm is using lvm, then it should be pretty straightforward.
Add more disk (through vSphere)
Fdisk to create partition
umount the existing partition
Add partition to the pv (pvcreate /dev/sdx)
Expand the vg (vgextend /dev/sdx)
Expand the lv (lvextend /dev/sdx)
Expand the filesystem (e2fsck/resize2fs)
Also, if you're not accustomed to doing this work, take precautions. I'm a fan of backups and snapshots and whatnot. Practice on something less-than-mission-critical, first. Perhaps a clone of this very box.
One of my preferred methods is to clone the subject, perform the work, and then if that works, just leave the clone running as the replacement and the original machine off.