How do I check my transformer of my oil furnace unit working fine then just quit.I tried direct wire eliminating the t-stat however no results please assist

To check a transformer you need a multimeter. A cheap electronic display type will do fine.
Set the meter to AC 250-400 volt range and measure the input voltage (110-220 Volt).

If there is no voltage, the problem is in the supply line of the transformer.

If there is input voltage, than check the transformer lable to see what the output voltage should be. Than measure the output voltage. If it is there, the problem is in the equipment connected to the transformer. If it is not there, the transformer is faulty.

If you need more information, contact me.

Success !

:)