Nest Learning Thermostat compatibility with Oil fired boiler

It's mostly the lack of the common wire. Those things eat power -- you should check that the transformer you have can power it OK. If it can, you can run the third wire. There are also some widgets available which are alleged to supply the third wire using the existing two wires; I've not had any experience with them.

You don't say whether you have steam or hot water heat. There seems to be some variance of opinion, but in general Nests -- and other learning thermostats which set the temperature back when the spaces are unoccupied -- don't play well with steam, as steam doesn't like setbacks. They play a little better with hot water -- but there are better ways to control hot water heat which really do save fuel. Nests and their kin are really intended for forced hot air.

Yes -- hot water. Don't be embarrassed -- we're sort of nuts about heat around here, but most folks aren't! The Nest will work OK for hot water, though.