Confusion about the term 'organic'

If a compound which did contain carbon, oxygen and nitrogen suddenly had an ion of magnesium in it (provided it is directly bonded to the carbon) then it is classed as organometallic, however, the use of the word organic to describe compounds nowadays is thrown around and many compounds fall under several umbrellas. Organic is strictly a carbon skeleton with no metallic contents. Inorganic compounds would be compounds such as NaOH, MgO, AlH3 etc. A good example of a compound that contains "organic" elements, but isn't strictly classed organic would be examples of Grignard reagents, these are organometallic. R-MgX, R being an alkyl group, X being a haloalkane. That Alkyl group could be anything ranging from a methyl group to larger chains and arenes (within reason). Bit of a dodgy answer, but then again, a dodgy question has a dodgy answer.