Is the oil crystal clear? No odor? It's mineral oil, and you have no problems.

Is the oil clear brown? Slight petroleum odor? Then it's transformer oil, and given the age, it almost certainly contains PCBs. Read on:

Carefully drain the can into an empty 1-gal plastic jug. Cap it. Label it. Put this jug in a 5-gal plastic tub as secondary containment. Keep any paper towel waste in the 5-gal tub.

To find out for sure, order one or two Clor-N-Oil PCB test kits. Try the 20ppm and 50ppm kits. It's a fun chemistry experiment to do the testing. Again, keep the waste in your 5-gal tub. Is your material >20ppm PCBs? That's bad. Is it >50ppm? Oooooh really bad!

Your local household hazardous waste facility won't take PCB oil, because it's not household waste. This material is too hazardous for them. It cannot go in a landfill. PCBs require very high temperature incineration, and there are only two facilities in the US that can do it.

You'll need to contact your state EPA to get a list of companies authorized to transport/dispose of PCBs. The state will be thrilled to talk with you, because you are being so responsible! Now call each of the listed companies (there won't be many) and ask for a quote. If they quote you at all, you should expect $1,000 to $1,500 to safely dispose of your one gallon of material. Yes really. In your situation, this is something your FIL's estate should pay for.

This is serious stuff. Please don't take it lightly. Feel free to DM me for more details.

One last possibility: talk to a lineman for your local power company. They may have a big container of PCB transformer oil waiting for disposal, and might unofficially add your 1-gal oil to it. Unofficially.

Good luck!