What oils can be used on a breakbarrel?

Neither. There are special non flamable oils for air guns. The high temp of compression will ignite petroleum based lubes and turn your air gun into a firearm and will damage it. It should tell you in your owners manual. Lube requirements are different for some guns. Here is a good selection of air gun products:http://www.pyramydair.com/a/Accessories/Cleaning_and_maintenance/18/cat_21
Also WD40 is not a lubricant it is a "W"ater "D"isplacer and penetrating fluid. It has very poor lubricating properties and evaporates quickly.
Air gun barrels need very little in the way of cleaning compared to powder burners as there are no combustion by products like carbon.