I was telling Jennifer about being able to request medals or replacement medals for family members from the various branches of service (I've requested ones for my father's service in WWII). The National Archives provides tons of interesting information...
3. How can I get my medals or those of my family?
NPRC (MPR) does not issue service medals; that is a function of each military service department. Nevertheless, veterans may request issuance or replacement of their medals and awards. Family members may only request medals and awards of living veterans by obtaining their signed authorizations. For deceased veterans, requests will be accepted from next-of-kin (unremarried widow or widower, son or daughter, father or mother, brother or sister of the deceased veteran). Military Awards and Decorations contains instructions and addresses for submitting requests. A sample authorization is also included for review.
To request, hit the link below. It looks like to get Oscar's medals, Jim and John will have to request them, as grandchildren are not eligible to request, the way I read the page.
There's also a neat Cold War Certificate that it looks like Jim would be eligible to receive for his service with a written request as well.