I guess if there was a big leak, you would smell it... but no harm in getting down & dirty & check your tank if you can... is it a plastic tank? Check the underbelly of it, just fold a clean dry cloth in your hand & follow the seam on the tank. The checked the support pillars for dampness. Also any pipes coming out of the tank - see if they are damp with the oil...
If you can, put a lock on the tank - won't stop someone per se from taking the oil, but at least you'll know if it was as the lock would be snapped.
Re the boiler, I had an old one myself & it was drinking the oil, without much return from it, pushed me to upgrade a few years back... I know there are loads on AAM who would be able to offer advice re the boiler...