How can I seal an old wood finish on a 60-year-old wall that is off-gassing?
60 year-old wood should not be "off-gassing." I suspect there's moisture behind the wood and you're dealing with mold and wood-rot. Did the home inspection note anything about it?

I would hire a indoor environmental service to test the air near the wood to determine the problem. If it is moisture, you need to get the leak fixed, lose the wood, fix the structural damage, treat for termites and then finish up with drywall and wainscotting or paneling.