I'm just wondering if the dog rubbed against the walls or stairs, and even if they cleaned it, the oils or odor remained.  

It isn't uncommon to give tenants free heat(oil) in my area.

Anyone who tells you they've seen everything in this business is either fairly new to it.... or a snake-oil peddler.At the end of the day, it sounds like many of you have had bad experiences with Property Managers.... and I'm truly sorry about that.

A tenant's vehicle leaked oil on the asphalt driveway of a rental property. 

Often the trash is in the wrong can, trash in recycling, and one time oil in recycling(said auto parts store told them to do it).

People have this crazy idea perpetuated by "gurus" that investing in real estate is easy and that they should be able to kick back on the beach somewhere day 1 and just watch the rent checks roll in ... while this may be the end game, you'll need to work your tail off to learn enough and build your portfolio large enough to get to that point ... trying to bypass that hard work by claiming to be "not handy" or any other excuse is inviting trouble IMO, usually in the form of scoundrels selling snake oil by telling you what you want to hear in order to part you from your hard earned money. 

I'm closing on a 1900 five-family with a relatively new oil boiler feeding a steam system.

I have a duplex (I live in half) with completely separate utilities and fuel oil furnaces.

It is not "snake oil."

I am a kilz fan for hiding dark shades, but the oil based I avoid unless battling something nasty, so try lower VOC)..