A.I feel that giving a 16-year-old dog any vaccinations is totally unnecessary. Even with rabies, through it’s legally required in most states every three years, there is a fairly decent chance of getting a legal exemption due to age, especially if your dog is not due until he is even older.
There is no reason to get any vaccine related bloodwork performed, except for rabies, to help you get an exemption; if you do, it will most likely indicate ample protection. As far as heartworm prevention goes, that depends on where in the country you live and the true incidence there. You’ll need to do some local research to determine a more educated decision on that one.