The tool at Smith’s Tavern is a long neck oil can used by the New York Central Railroad (NYCS). Adjacent to the handle is a screw cap opening into which the oil was added.
Hand oilers were used by railroad engineers to lubricant the locomotive and/or other train cars. It is noted in the reference material that these types of oilers were deemed too big (holds 2-3 pints of oil) as the average locomotive needed about only one pint to lubricant the average engine. The contra point is that a large oiler didn’t require frequent refilling.
Reference: Railway and Locomotive Engineering: A Practical Journal of Railway Motive Power, Rolling Stock and Appliances, Volume XXVIII, 1915, page 149.